Dempsey said that he was not going to press the Iraqi government about its involvement in helping Iran send supplies to the Syrian regime of President Bashar Asasd.
Iraq has seen a string of attacks from militants since the last U.S. troops left in December; al Qaeda in Iraq (AQI) has claimed responsibility for attacks in July that left more than 160 dead. The country has also faced political turmoil between al-Maliki and Iraqi opposition groups.
Republicans defense hawks in Congress were critical of the U.S. decision to remove all troops last year, but the Obama administration has said it wound down the war in Iraq responsibly.
Dempsey came to Iraq from Afghanistan, where his plane was damaged by shrapnel from rocket fire at Bagram air base early Tuesday morning. Dempsey was not on board at the time and was not in danger.
Dempsey, who had to use a different plane to travel to Iraq, told AFP that it was perhaps a “lucky shot” by the Taliban.