A statement says the Multi-National Division - Baghdad soldiers were killed in an indirect fire attack just after 1 p.m. Monday in an eastern section of the capital.
The statement didn't give an exact location for the attack but the area has been the scene of intense fighting recently between Shiite militiamen and U.S.-Iraqi troops.
At least three militant mortar attacks hit the Green Zone in central Baghdad Monday; In Sadr City - the stronghold of the Mahdi Army militia - U.S. soldiers battled deeper into the district a day after fierce clashes that killed at least 38 suspected militants, the military said.
U.S. soldiers killed seven more extremists Monday after coming under small-arms fire in Sadr City, the military said. Four of the suspects were killed in an airstrike and three others by an Abrams tank crew, according to a statement.
Sadr City has become the center of a showdown between the Iraqi government and the Mahdi Army, which is led by anti-American cleric Muqtada al-Sadr. U.S. forces have been increasingly drawn into the battles - including operations seeking to curb a rise in mortar and rocket attacks on the Green Zone.
On Monday, 30 Iraqi lawmakers from various political parties urged Iraqi Prime Minister Nouri al-Maliki to end the monthlong confrontation, saying innocent civilians and children were the main victims of the fighting.
"Yes, you can do it if you remember your own children," said a joint statement read by Mustafa al-Heeti, a Sunni member of parliament. "Your people (are) are demanding of you to intervene and solve the crisis peacefully."
Their appeal came after U.S. forces, backed by Abrams tanks and Bradley armored personnel carriers, fired on insurgents positions in Sadr City. The military said 38 militants were killed. Iraqi health officials said 58 people, including five children and eight women, were injured.
The fighting erupted after militants took advantage of a sandstorm to unleash a barrage of 107 mm rockets and 82 mm mortar shells at the Green Zone, which includes the U.S. and British embassies and some key Iraqi government offices.
The near-daily shelling of the Green Zone has become acutely embarrassing for both Iraqi authorities and the U.S. military.
Rather than mount an all-out assault, U.S. commanders have tried to limit the shelling by walling off the southern third of Sadr City and trying to put the Green Zone out of range of light rockets and mortars.
Chinese-made 107 mm Katyushas have a range of about five miles, while 82 mm mortars can exceed three miles. Much of the Green Zone is more than five miles from firing positions beyond the new wall.
"It's a tried and true strategy that we'll continue to prosecute here because it has worked well in other locations, and we think it'll work well here," said Brig. Gen. Will Grimsley, an assistant division commander.
Col. John Hort, who commands U.S. troops on the southern edge of Sadr City, said the heavy sandstorm sharply limits sensors and targeting lasers on helicopters and unmanned drones used to identify firing positions.