BAGHDAD, Iraq — Four American soldiers were killed in two rocket attacks in Baghdad yesterday as clashes between American-backed Iraqi forces and Shiite militiamen intensified, the military said.

Three soldiers were killed about 1 p.m. in eastern Baghdad, where fighters loyal to anti-American Shiite cleric Muqtada al-Sadr have battled American and Iraqi troops. The fourth American soldier was killed at 4:15 p.m. in the western part of the capital, a U.S. military spokesman said. The military provided few other details about the attacks.

The deaths marked one of the deadliest days for American troops in Iraq since Prime Minister al-Maliki launched an offensive against Shiite militias in the southern city of Basra in late March, prompting retaliation there and in the vast Shiite district of Sadr City in Baghdad. Forty-four American troops have died in Iraq in April, according to iCasualties.org, which tracks military fatalities, more than any month since September.

Also yesterday, militiamen launched a mortar and rocket attack against a combat outpost in Sadr City shortly after several top military officials, including Brigadier General William Grimsley, had visited. Fifteen American soldiers were injured in the attack, none seriously, a U.S. military spokesman, said Lieutenant Colonel Steve Stover, said.

“We will continue fighting to get a safe environment and neighborhood for the citizens of Sadr City,” Mr. Grimsley told reporters during his visit to the outpost.