BAGHDAD - Two American soldiers died of wounds by insurgent attack in Iraq, the US military said Sunday.

"Two US service members died April 2 of wounds suffered when enemy forces attacked their unit with indirect fire," the military said without giving further details about the exact location of the incident.

"Indirect fire" usually refers to mortar or rocket attacks in the terminology of US military statements.

The names of the deceased are being withheld pending notification of next of kin, the statement added.

The latest deaths brought the death toll of US soldiers in Iraq since the war broke out in 2003 to 4,443, according to media count based on Pentagon figures.

In mid 2010, US troops in Iraq were reduced to below 50,000 soldiers. Washington said the remaining US troops in Iraq are conducting support and training missions.

U.S. military forces are to pull out completely from Iraq by the end of 2011, according to the security pact named Status of Forces Agreement, or SOFA, signed late 2008 between Baghdad and Washington.