The US Embassy said the area was hit by indirect fire, the military's term for rocket or mortar attacks, and said there were "no reports of serious injury or deaths at this time."
Armed groups attacked several checkpoints and the US-protected Green Zone on Sunday.
The fighting escalated as anti-US cleric Muqtada al-Sadr, rejected terms set by the Iraqi government for lifting a crackdown against his Mahdi Army.
The clashes on Sunday were concentrated in Sadr City, the stronghold of the Mahdi Army, where US soldiers used Abrams main battle tanks to repel the attackers.
Iraqi and US soldiers came under attack "by a large group of criminals," the US military said.
Fifty-eight people, including five children and eight women, were also injured in clashes in Sadr City since Sunday, local health officials said on Monday.
US death toll
The latest deaths bring to at least 439 the number of fighters and civilians killed in a month of clashes in Sadr City, where violence erupted after Nuri al-Maliki, the Iraqi prime minister, ordered a countrywide crackdown on Sadr followers, starting in the southern oil city of Basra.
Three US soldiers were killed on Monday in eastern Baghdad, the American military said.
The soldiers were killed in an attack at around 1pm (1005 GMT), a military statement said.
At least 18 US soldiers have died in Baghdad since the clashes began.