Iraqi security officials and medical sources said another 17 people were also wounded in the fighting in Sadr City.
There was no immediate word from the US military.
Hundreds of people have been killed in the clashes which began on March 25 and followers of al-Sadr have accused the US military of killing civilians.
The US military charges that the fighters have been using civilians as human shields.
Marines' deaths
The deaths of the US soldiers occurred when their vehicle was hit by an improvised explosive device on Friday.
The attack marks one of the deadliest attacks against US troops in the mainly Sunni province in months, the military said on Sunday without specifying the exact location of the ambush.
The attack came 10 days after a similar ambush in Anbar in which two US marines were killed and three wounded.