The three were seized early yesterday from a house in Mansour, an affluent suburb where several embassies and foreign companies are based.
The latest kidnappings add to a sense of growing insecurity prompted by months of violence in Iraq and come as a US government security analysis showed that Washington is gloomy about Iraq's stability.
The security memo, the National Intelligence Estimate, which is based on a compilation of views from various intelligence agencies, says that the prospects for Iraq's immediate future range from a tenuous political, economic and security situation at best, to all-out civil war at worst.
Meanwhile, even Republican senators branded the administration's reconstruction efforts "beyond pitiful" after the White House sought to divert $3bn (£1.67bn) earmarked for reconstruction to bolster security. The Bush administration dismissed the critics as "pessimists and hand-wringers".
President George Bush yesterday also attempted to deflect the criticism of the UN secretary general, Kofi Annan, who described the war in Iraq as illegal.
Speaking at a rally in St Cloud, Minnesota, Mr Bush said: "The UN looked at the same intelligence that I looked at. They concluded that Saddam Hussein was a threat and they voted by 15 to zero in the security council for Saddam Hussein to disclose, disarm or face serious consequences. I believe that when bodies say something they better mean it."
US officials last night confirmed that the three missing men were civilians working for Gulf Services Company, a Middle East-based construction firm. The two Americans were named as Jack Hensley and Eugene "Jack" Armstrong.
"Unknown gunmen" had seized them from their residence in Mansour along with a British subject, the officials said.
"The US government is using all available means to locate them. The Iraqi government is also fully assisting," said Vicki Stein, a spokeswoman for the US embassy in Baghdad. A British diplomat in Baghdad was unable to confirm any details.
Witnesses said that a group of men had pulled up outside the house early yesterday in a van and another vehicle and waited.
"At 6am the power failed in our road. Two of the foreigners left their house and went into the street to start the generator," said Bahar Salim, a 19-year-old student who lives nearby.
"These guys then grabbed the two foreigners. They then went into the house and pulled out the third westerner who had been sitting inside. No shots were fired. It was all over in minutes. I looked inside afterwards and saw that the computer was still running," he added.
Mr Salim said the Briton and American had employed two unarmed security guards who had vanished two days ago.
Yesterday's kidnapping follows the abduction 10 days ago of two Italian women aid workers, Simona Pari and Simona Torretta, both 29, who were seized from their Baghdad offices in daylight by an armed gang. Their kidnapping sparked panic among the dwindling number of foreign journalists and diplomats still in Iraq.
Two French journalists taken hostage last month are unaccounted for. In an ominous development, French diplomats yesterday collected the reporters' belongings from their Baghdad hotel.
Last night, Iraqi police said they had found a corpse north of Baghdad believed to be that of a western man dead for some days.