BAGHDAD, July 2 (Reuters) - Two U.S. soldiers were killed in the Iraqi capital Baghdad on Sunday, the U.S. military said on Monday. The military said one soldier was killed by small arms fire in southern Baghdad. The second soldier was killed by gunfire that followed a roadside bomb attack on his patrol in western Baghdad. Two Iraqi policemen were also wounded in that attack. June was costly for U.S. forces, with 101 soldiers and Marines killed. That made the April-June quarter the bloodiest since the U.S.-led invasion in 2003. Around 3,580 American soldiers have been killed in Iraq. Many tens of thousands of Iraqis have also lost their lives.