The attack began when one bomb went off as a U.S. unit was returning from a search operation in the mostly Shiite area, the military said. Moments later, a second bomb exploded, killing and wounding the soldiers.
A demolition team that searched the site after the attack found an explosively formed projectile, a type of high-tech bomb which the U.S. military believes comes from Iran. The device was detonated by the team.
Earlier Thursday, the military said a U.S. soldier was killed the day before in combat in Anbar province, west of Baghdad.
In addition, a Marine assigned to Multi National Force-West also died Wednesday in a non-combat related incident in Anbar, the military said in a separate statement. It did not give more details, saying the incident is under investigation.
Earlier Thursday, a suicide car bomber apparently targeting a senior city official sent a ball of fire tearing through a busy square in a mainly Shiite area in Baghdad on Thursday, killing at least eight people.
The driver detonated his explosives as a convoy carrying the head of the Baghdad city council, Sabir al-Issawi, was passing an Iraqi military checkpoint in the central Karradah neighborhood. The council chief was unharmed, but three of his bodyguards were wounded, his deputy, Naeem al-Qabi said.
Nobody claimed responsibility for the attack, but suicide car bombings are the hallmark of Sunni insurgent groups, particularly al Qaeda in Iraq. It was the second devastating blast to hit the thriving commercial district in four days. An explosives-laden car rammed a flatbed truck packed with Shiite pilgrims there on Sunday, killing 32 people.
In other developments:
Qassim Ismail, who owns a kiosk that sells cigarettes and soft drinks, was wounded by shrapnel Thursday and knocked unconscious.
"I have been working in this place for four years and have witnessed many explosions ... but I can't leave my work because I have family and live nearby," he said from his hospital bed.
The attack was a fresh example of what the U.S. military is now calling its biggest challenge in cracking down on the sectarian violence in Baghdad — car bombs, which killed at least 14 people in and around the city on Thursday.