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.
In addition to the Karradah attack, a bomber slammed his explosives-packed car into an army checkpoint in a volatile Sunni district in western Baghdad, killing two people and wounding two.
A bomb in a parked car exploded as a bus packed with workers passed by in the city of Iskandariyah, 30 miles south of Baghdad in the so-called "Triangle of Death," killing at least four people and wounding 24, police said.
The top official in the main Shiite district of Sadr City was seriously wounded when gunmen ambushed his convoy in eastern Baghdad, killing two of his bodyguards, according to police and a local official. Rahim al-Darraji had been involved in negotiations with U.S. and Iraqi government officials seeking to persuade the Shiite militias to tamp down the violence against Sunnis.
Police reported at least 25 other people were killed or found dead Thursday, including a vegetable seller who was hailed as a hero after he died when a bomb concealed in a package exploded as he was trying to carry it away from a populated area in Sadr City.
"May God bless his soul. He gave his life to save other lives," fellow peddler Haitham Mohammed said, wiping away tears.
Twenty bullet-riddled bodies also were found, most of them in Baghdad, a small number compared with the average of 50 that were turning up before the Baghdad security plan. Most were believed to be victims of Shiite militias led by the Mahdi Army loyal to radical cleric Muqtada al-Sadr. The drop in execution-style killings is in large part because Shiite parties have been successful in persuading the Shiite militias to pull armed fighters off the streets to avoid a showdown with the Americans. Many fear the fighters will re-emerge if the U.S. forces leave.
In other developments, a judge said the death sentence for Saddam Hussein's former deputy, Taha Yassin Ramadan, had been upheld on appeal, and the former vice president will be hanged for his role in the killing of 148 Shiites in 1982 in Dujail, north of Baghdad.
Judge Mounir Haddad, a member of the court's nine-judge panel, said the decision on Ramadan's execution was unanimous and relayed to Prime Minister Nouri al-Maliki's government, which will set the date.
The panel ignored appeals from international human rights groups. Human Rights Watch and the International Center for Transitional Justice said the evidence was insufficient for such a punishment. Ramadan was convicted in November along with Saddam and six others in the killings of Shiites in Dujail following an assassination attempt against the former Iraqi leader in 1982. Three other defendants were sentenced to 15 years in jail in the case, while one was acquitted.
Saddam was hanged Dec. 30, and two of his co-defendants in the Dujail case — his half brother and former intelligence chief Barzan Ibrahim, and Awad Hamed al-Bandar, former head of Iraq's Revolutionary Court — were executed in January.
The Shiite-led government also announced plans for a minute of silence across Iraq on Friday to commemorate the anniversary of the 1988 chemical weapons attack on the Kurdish town of Halabja in northern Iraq, according to state TV. Saddam ordered the attack as part of a scorched-earth campaign to crush a Kurdish rebellion in the north.