Witnesses said the blast sent victims flying in front of the terminal building at Davao airport on Mindanao island, in southern Philippines, where 260 US troops have been training local security forces in jungle warfare and anti-guerrilla operations.
One American missionary was killed and three others, from a Southern Baptist missionary family, were among the wounded.
A spokesman for President George Bush said: "The United States will work shoulder to shoulder with the Philippine government to make certain that those responsible are brought to justice."
No one claimed responsibility for the blast, but President Gloria Macapagal Arroyo said "several men" were detained. The military has blamed Moro Islamic Liberation Front (Milf) rebels for a string of attacks, including a car-bombing at nearby Cotabato airport last month that killed one man.
Eid Kabalu, the spokesman for the group, which has been fighting for Muslim self-rule in the predominantly Roman Catholic Philippines for more than three decades, denied his group was responsible. He condemned the attack and said his organisation was ready to cooperate in an investigation.
Only hours earlier the mayor of Davao, the Philippines' second city, had thanked the group for sparing the city from its bombing campaign.
The blast comes at a time of heightened local tension over the role of US troops in the war on terror in the Philippines, where Muslim insurgents have fought the government for decades with attacks, bombings and kidnappings.
With many of the injured in serious conditions, officials said the dead so far were a boy, a girl, 10 men and seven women, but the number could grow.
Scores of people were huddled in the shelter, escaping a downpour as they waited for arriving passengers, when the blast blew off the iron roof.
Terry Labado, an airport official, said: "I saw bodies flying [and] people lying on the ground. They looked dead."
An airport security official, who did not want to be identified, said the bomb rocked the front of the terminal building, smashing windows and causing considerable damage.
"It happened ... a few minutes after a Cebu Pacific flight arrived and people packed the waiting area. There were many people killed. I saw six persons killed on the spot," he said.
American troops went to the Philippines last year - their first expansion of the war on terrorism outside the fight with al-Qaida in Afghanistan. Some 1,200, including 160 special forces personnel, were sent to "train, advise and assist" Philippine forces battling Abu Sayyaf guerrillas on the island of Basilan.
Last month, US defence officials announced they had an agreement to deploy more than 1,000 troops in an effort to rout the remaining Abu Sayyaf forces from the nearby island of Jolo. But the offensive was put on hold after Pentagon officials described the deployment as "joint operations" that would have drawn Americans into battle.
That wording caused an uproar in the Philippines. Newspapers, MPs and leftwing groups accused the government in Manila of violating the constitution that bars foreign troops from combat. Manila repeatedly denied there would be a US combat role, saying Americans were coming for a training exercise.
President Arroyo said she "strongly condemns the Davao bombing as a brazen act of ter rorism which shall not go unpunished".
It was not the only violence to hit the mainly Roman Catholic nation yesterday. Soon after the airport explosion, a grenade attack wounded two people in the nearby town of Tagum.
Security has been heightened in recent weeks as government forces crack down on Milf and three other rebel groups seeking an Islamic state.
A few weeks ago, Philippine soldiers overran a key Milf stronghold near the town of Pikit in central Mindanao. Several bombings since then, including an attack on power pylons, have been described as reprisal attacks by Milf.
Military officials said the latest explosion may fit this pattern.