The resulting gunfight killed an attacker and a guard, according to U.S. and Iraqi officials, the Associated Press reported.
The U.S. Embassy confirmed that an American had been abducted in the shootout, which occurred about 5:30 p.m. in the upscale Mansour district of western Baghdad, but did not identify him.
Police Lt. Col. Maan Khalaf said the attackers arrived in three cars around iftar, the traditional sunset meal that breaks the daylong Muslim fast during the holy month of Ramadan.
The kidnappers stormed the two-story house, surrounded by an outer wall with iron bars, and forced the victims to leave with them.
A neighbor, Haidar Karar, said he saw from his house "at least 20 attackers, some masked and some not." He said some were wearing traditional Arab robes and all were carrying automatic weapons, according to the AP.
Late Sunday, as Iraqi interim Prime Minister Iyad Allawi warned of a "military solution" to inconclusive peace talks with Sunni insurgents, a rocket exploded into the Sunubar Hotel in Tikrit. The explosion killed 15 Iraqis and wounded eight others, according to the AP.
The U.S. military said "anti-Iraqi forces," caused the attack.
Saturday became the deadliest day for American forces in six months when nine U.S. Marines were killed and nine others wounded in a car bomb explosion beside a truck in the Anbar region of Iraq.
The Anbar region, located southwest of Baghdad, extends to the borders of Syria and Jordan and includes Fallujah, an insurgent stronghold. Insurgents frequently attack U.S. forces on patrol in the Anbar region with car and roadside bombings.
Meanwhile, peace talks in Fallujah started to wind down over the weekend as the insurgents and the interim Iraqi government failed to come to an agreement.
"We have now entered the final phase of attempts to solve Fallujah without a major military confrontation. I hope we can achieve this, but if we cannot, I have no choice but to secure a military solution," Allawi said Sunday. "But I owe, owe it to the Iraqi people to defend them from the violence and the terrorists and insurgents."
Iraqi and U.S. forces are trying to put down the insurgents, who have controlled Fallujah since April, before the scheduled Jan. 31 election. The U.S. military is preparing to launch a major offensive in Fallujah and Ramadi when it gets the green light from Allawi.
"We are gearing up to do a major operation, and when we are told to go, we will go," said Brig. Gen. Dennis J. Hujlik, deputy commander of the 1st Marine Expeditionary Force, the Washington Post reported.
Roughly 50 religious leaders met with the Shura Council of Mujaheddin, a self-appointed group that governs Fallujah, to discuss the impending offensive. According to an anonymous Washington Post source, the group agreed to issue a religious order calling for a holy war if U.S. forces started an offensive in Fallujah.
As of Sunday, at least 1,120 U.S. military members have died since the beginning of the Iraq war in March of 2003, according to the AP.