Meanwhile, Iraqi Prime Minister Nouri al-Maliki on Wednesday accused the Mahdi Army, loyal to Shiite cleric Muqtada al-Sadr, of using humans as shields and vowed to continue his crackdown on militias.
Two U.S. soldiers died in northwestern Baghdad from a roadside bombing and from small-arms fire. A third soldier died in a roadside bombing east of the capital city, according to the military.
An Associated Press tally shows that at least 4,059 members of the U.S. military have died since the March 2003 U.S.-led invasion of Iraq.
"We have said all along that this will be a tough fight and there will be periods where we see these extremists, these criminal groups and al-Qaida terrorists seek to reassert themselves," U.S. military spokesman Maj. Gen. Kevin Bergner told reporters in Baghdad, the AP reported.
At least 10 gunmen had been killed in three separate clashes in eastern Baghdad on Tuesday and Wednesday, the military said.
The latest fighting erupted in late March when al-Maliki launched a crackdown against Shiite militias in the southern port city of Basra, but it spread to Baghdad's Sadr City neighborhood, which is a stronghold of the Mahdi Army.
Militia fighters have used the area as a base to launch missiles and mortars at the Green Zone, which houses most of the Iraqi government and Western diplomatic missions.
On Wednesday, al-Maliki, who himself is a Shiite, grouped the Mahdi Army in with groups such as al-Qaida that should be dissolved.
He set four conditions -- that the militia disarm, stop interfering with state affairs, stop running their own courts and hand over wanted fugitives -- or face a military assault, Reuters reported.
"To refuse these conditions means the continuation of the government's efforts to disarm them by force," al-Maliki said at a news conference in the Green Zone.