The following correction was printed in the Guardian's Corrections and clarifications column, Thursday 28 May 2009

The feature below on Desmond Tutu listed other Anglican preachers who stood against apartheid in South Africa. Included was Denis Hurley, who was a Roman Catholic.

They call him Father, but as he sits at the breakfast table eating Cheerios with fruit and yogurt, giggling as he teases and is in turn teased, Archbishop Desmond Tutu looks more like a mischievous little boy.

"Are you going to wear that shirt?" asks Lynn Franklin, his literary agent and friend, with whom he is staying on Shelter Island, a holiday retreat in the Hamptons, New York State.

Tutu widens his eyes and opens his mouth in mock indignation. "What is wrong with this shirt?" he says, looking down at his dark blue T-shirt.

"How about the one I ironed for you?" Franklin says.

"But this one has the logo for the World Cup," says Tutu, pointing to the small emblem on his chest, before turning to me. "Tell your photographer not to go below the belt," he says.

As I struggle to work out what he means by this, he gets up from the table to reveal a pair of little legs poking out of the bottom of a pair of long shorts. The cassockless figure that makes his way back through the kitchen has an air of Clark Kent about him - posing as a civilian but ready to use his powers for good. Less like a Nobel laureate than, well, your father, only on holiday.

Except it doesn't seem like much of a holiday. Tutu, now 77, has been saying he plans to wind down and lead a more contemplative life for the best part of a decade, particularly after he was diagnosed with prostate cancer 12 years ago. But here he is, almost 8,000 miles away from his home in Cape Town. He's supposed to be taking a break, but the previous day, and the day before that, he was giving television interviews. Today he's with us. A week later, he'll cross the ocean to appear at the Hay festival.

"In many ways, when you're a Nobel peace laureate, you have an obligation to humankind, to society," Tutu says in his slow, deep, deliberate voice. "And you are able to say things that people might take more seriously than if you were not a Nobel laureate. And with a world that faces so much conflict and suffering, there seems to be a place for those who just might help us change tack. But I am still deeply longing for a quieter life. And I really mean it when I say it. I'm really going to try. My wife says that she's heard me say that several times. I will try next year and be ruthless. But what do you say when the prime minister of the Solomon Islands writes and says, please, could you come and be with us when we launch our truth and reconciliation commission? It seems so rude, so hard-hearted in a way, to say no and have them think, 'We are a small nation. Perhaps we don't count for a great deal.' If you do go, it just might lift their morale."

Given that the Solomon Islands are also 8,000 miles from Cape Town, he could reasonably say, "No. I'm over 70 and you're a long way away, but I wish you luck and my prayers are with you." Perhaps not doing that is what distinguishes a Nobel peace laureate from the rest of us. Nonetheless, it is a tremendous burden, bordering on conceit, to think that Tutu might take personal responsibility for global conflict and suffering.

"It would be utterly presumptuous to think, off one's own bat, that one would be able to accomplish something as awesome as that," he says. "I certainly know that I would not be able to survive if it were not for the fact that I am being upheld by the prayers of so many people."

Tutu is indeed up there with the Dalai Lama as one of those figures who had their moral stature minted in one specific context and managed to convert it into an international currency that never seems to lose its value. In Tutu's case, the context was apartheid South Africa, where he was appointed the first black dean of Johannesburg in the mid-70s. Given that the deanery was in the white part of town, Tutu would have needed a permit to live there. He decided, instead, to make his home in the township of Soweto. "I probably would have got permission from the government," he once said, "but it would have been as an honorary white, and Leah [his wife] and I decided we were not going to humiliate ourselves in that way. We said to the cathedral that we would live in Soweto. It caused a row in the press."

Shortly afterwards, he sent a letter to the then prime minister, John Vorster, warning him that something cataclysmic was brewing. Vorster ignored him. Not long after came the Soweto Uprising, when black youths came out en masse to resist the regime's attempt to force them to learn in Afrikaans - the language of the Boer white minority.

"When a pile of cups is tottering on the edge of the table and you warn that they will crash to the ground," he once said, "in South Africa you are blamed when that happens."

So Tutu, among others, got the blame. And thus began his domestic reputation as a rabble-rouser and troublemaker and, internationally, as a clear, forthright and perspicacious voice against injustice. At a time when the African National Congress's leadership was either in jail or in exile, there was Tutu - cassock flowing, crucifix swaying front and side, as he strode through the brutality of the townships and the mendacity of apartheid. Delivering blistering attacks on the regime one minute, diving into a crowd to save a suspected "informer" from being necklaced the next. During the transition, he chaired the Truth and Reconciliation Commission: a moral, spiritual conscience to complement Nelson Mandela's political, strategic vision. A feisty individual in his own right, Tutu was also part of a tradition of radical Anglican preachers in South Africa who made a stand against apartheid, among them Trevor Huddleston, Michael Lapsley, Paul Verryn, Njongonkulu Ndungane and Denis Hurley.

Tutu has claimed that his greatest weakness is that he loves to be loved. "There are not too many who enjoy being castigated as ogres," he says, "as someone others love to hate. I think that most of us would prefer to be popular than unpopular. I know for myself that it has tended to be a weakness - a tendency to enjoy the limelight, a weakness that would make you soften things that are hard but that you need to say. Many people would be surprised that, in fact, I'm quite shy. I know it doesn't look like it."

I smile. It is a common refrain of extroverts that they are, in fact, instinctively withdrawn and inclined to overcompensate. The late Archbishop of Canterbury, Robert Runcie, a good friend of Tutu's, once described him as "a bit of a showman". He has been known to bust out a dance move whether or not there is a dancefloor in sight. At the very least, he is the most outgoing introvert I have met. Tutu notices my scepticism.

"Look at your smile," he laughs. A big belly laugh that lies somewhere between Sid James and Santa Claus. "You're thinking, 'Wow', but I'm not quite as ebullient as I seem. One of the weaknesses of wanting to be loved is that you hate being confrontational. There are many situations in which one finds oneself where you have to be confrontational, and that is contrary to my temperament." More laughing. "Many would say, 'What?! When you can be so strident and acerbic in your attacks on others?' But it's put on."

It's all just a performance?

"Well, not in the sense that it's histrionics, but I have to get myself into that particular moment. And my inclination would be to keep quiet and not muddy the waters. I depend upon and am sustained so utterly by so many people, and I am fortunate enough to have been trained by a religious community for the priesthood and saw how crucial for them the spiritual life was - so one has sought to emulate them. Without that resource, I would have been done for long ago."

For all his professed reticence, this man who loves to be loved has an uncanny habit of upsetting all sorts of people. "If you are neutral in situations of injustice, you have chosen the side of the oppressor," he once said. "If an elephant has its foot on the tail of a mouse and you say that you are neutral, the mouse will not appreciate your neutrality." So there he has been, chiding the elephants and looking out for the mice. During the 80s, he called Ronald Reagan and his policies "racist" and said that the west "can go to hell". He called former apartheid leader PW Botha a liar and suggested he was a Nazi sympathiser. "I don't know whether that is how Jesus would have handled it," Tutu told his biographer, John Allen, "but at that moment I didn't actually quite mind how Jesus would have handled it. I was going to handle it my way."

His criticisms were not reserved for apartheid South Africa. He has called on Robert Mugabe to resign or be sent to the International Criminal Court in The Hague for "gross violations", he has expressed his "disappointment" in Tony Blair for the "immoral" invasion of Iraq, and his disappointment in the new Pope for being a "rigid conservative", and he has drawn parallels between Israel's treatment of the Palestinians and apartheid's treatment of blacks.

Tutu has also been quite stringent in his criticisms of post-apartheid South Africa. He told Mandela that he was setting a bad example by failing to make "an honest woman" of his now wife Graça Machel, with whom he had been in a relationship for more than a year before they got married, and he slammed former South African president Thabo Mbeki for surrounding himself with yes-men and for replacing an old white oligarchy with a biracial one.

"He speaks his mind on matters of public morality and has from time to time annoyed many of us who belong to the new order," Mandela once said of his old friend. "But such independence of mind, however wrong and unstrategic it may at times be, is vital to a thriving democracy."

Such is the record of this particular "shy" man that one wonders who else's feathers Tutu might have ruffled if he had been outgoing. It is a testament to both his charm and his authority that he has managed to court so much controversy and yet avoid its taint.

Most recently Tutu's ire has been reserved for the recently elected South African president, Jacob Zuma. When Zuma was lobbying for the leadership of the ANC, Tutu said, "I pray that someone will be able to counsel him that the most dignified, most selfless thing, the best thing he could do for a land he loves deeply, is to declare his decision not to take further part in the succession race of his party."

At the time Zuma had been charged with rape, after sleeping with an HIV-positive woman less than half his age, without using a condom. He was also alleged to have been involved in racketeering and fraud, although the National Prosecuting Authority dropped the charges, citing political interference. He defeated Mbeki in a bitter internal party feud in which the ANC membership vented their frustration at the slow pace of economic reform and Mbeki's distant and haughty manner. Supporters of Zuma, who was later acquitted of the rape charge, led a smear campaign against the woman who brought the charge.

"I for one would not be able to hold my head high if a person with such supporters were to become my president," Tutu says. "Someone who did not think it necessary to apologise for engaging in casual sex without taking proper precautions in a country that is being devastated by the horrendous HIV/Aids pandemic."

Zuma won the election with a resounding 66% of the vote and is now Tutu's president. When I read these quotes back to him, he chuckles. How is his head holding up now?

"I said that during his rape trial, when some of his supporters were saying quite unacceptable things against the woman who brought the charges against him," he says. "I would have thought that one would have remonstrated with them more forcefully than was the case."

He fears that the trial, and the way it was resolved, has produced a cloud that will for ever follow Zuma. "I think that many have felt uneasy about the fact that he had these charges hanging over his head. And it is also the way they were dealt with - not through a court, but administratively. So there will always be this shadow hanging over him. And that's a shame. But he is hugely popular with a large section of our community, so the thing to do is to wait and see - let us give him the chance to prove himself, hoping against hope that what we might have feared will not, in fact, eventuate."

As he weighs his words even more carefully, the clearcut moralism for which Tutu is renowned finally gives way to a more measured pragmatism. "It's water under the bridge. It's the new reality. He's been inaugurated. He's appointed a new cabinet. Let's see what happens. At this stage, I am perhaps neutral... I'm sad for my country. I think we could have done a great deal better in the way that we handled the differences... But then, politics is politics, and we have to live with these realities as they are."

The fact that Tutu is hoping against hope does not, ultimately, suggest that he is that optimistic. He is prepared to give Zuma the benefit of the doubt, but the doubts are still very apparent. "We are facing very serious problems. Like the rest of the world, we are facing the economic downturn, but we also have problems that are peculiar to us. There is a very high incidence of HIV/Aids. We are the epicentre in many ways. We have high levels of crime, levels of poverty that are unacceptable, and then the usual bangshoot of corruption and things of that sort. So they have a very full plate to deal with, one must wish them well for everybody's sake. They have to succeed."

He thinks some encouraging signs emerged from the handover from one president to another, although he feels that the new Zuma administration has been unnecessarily vindictive towards some of Mbeki's supporters. "One positive thing is that we are constantly castigating African presidents who want to be presidents for life. And I think the rejection of Thabo Mbeki going for a third time and somehow to ensconce himself as a president in perpetuity is a good thing. There was also a reaction to Mbeki's style. Many experience him as perhaps too English. He didn't carry his heart on his sleeve, as most of our people tend to do. He appeared to be aloof. Zuma, on the other hand, is warm and engages people. You can see, when he's dancing on the stage, people warm to him in a way that they didn't to Thabo Mbeki. So all of those factors militated against Thabo."

If political developments in South Africa have left Tutu somewhat jaded, then the election of Barack Obama in the US has made him very excited. "It's such a fantastic thing," he says. "He's filled Americans with a new pride in their country. Quite justifiably. But he's also filled the world. Everybody assumed that, once he came to power, there would be a new style in American politics, where previously they behaved like bullyboys. Everybody said, 'No, you shouldn't invade Iraq, give the UN inspectors more time.' And America says, 'Go jump in the lake.' They didn't sign the Kyoto protocol. They didn't sign the Rome statute on the international criminal court. Now people believe that we are going to have an America that is a leader of the world, not by being obstreperous, not by being a bully, but by being collaborative. Already you've seen a change in style. Just look at how the Germans turned out for him even before he won. Here, African Americans are walking with a new spring in their step... He has such a presence. He is presidential. He's warm. But you won't take any liberties with him. What a gift of oratory."

Haven't we been here before? Black people with a spring in their step, a nation rehabilitated abroad and, apparently, reconciled with its own racial history at home? For all the huge differences, doesn't the America Tutu is describing in 2009 sound a lot like the South Africa in 1994, with which he is now disenchanted?

"There is always a theoretical possibility of total disillusionment and disappointment," he says, "but I think that the indications are in the other direction. He's a very astute person. And I think he has sought to find those next to him, near to him, who are more than competent. He's shown that in things like shutting down Guantánamo Bay and appointing George Mitchell as his special envoy to the Middle East. The signs are propitious... But obviously, yes, maybe we could muck ourselves up by being unrealistic in our expectations... But it is important that he has filled people of colour with a new sense of who we are, and that is great."

There are other questions I want to ask. About the Truth and Reconciliation Commission and how it might relate to the US grappling with torture; about the children's book he has just written; and about the global group of Elders he chairs, which aims to apply its wisdom to conflicts in the global village.

But this particular elder is fading. As he leans back in the sofa, his speech slows and his eyelids droop. I ask a few questions anyway and he answers wearily. A man who has devoted his life to struggle is struggling to finish a sentence and keep his eyes open. The laughs become more muted. As we pack up, Lynn Franklin asks if he can spare 15 minutes tomorrow to do something else. Then Leah, his wife, calls. As I say goodbye, Tutu is on the phone and virtually horizontal. Sustained by prayer, a big cushion and a comfy sofa. Father needs a nap.

• Desmond Tutu will deliver the Hamlin Lecture at the Hay festival on Thursday 28 May. For further information on the Elmley Foundation series of Faith Lectures, go to hayfestival.com/faith. Tutu's picture book for children, God's Dream, is published by Walker