Iranian-supported militias make up the majority of ground forces now striking against the Islamic State of Iraq and Syria in the Iraqi city of Tikrit, in a growing shift of influence in the region even as the U.S. pours thousands of troops and millions of dollars in military equipment back into Iraq to bolster Baghdad’s efforts against the terrorist group.

“Iran’s influence is growing in Iraq,” commander of U.S. Central Command Gen. Lloyd Austin told the House Armed Services Committee Tuesday, in a day of congressional testimony from the Pentagon’s top leaders that gradually painted a picture that was heavy in its revelations about Iran’s role in Iraq, after years of little information on the issue.