SULAIMANIYAH, Iraq — While the United States has invested trillions of dollars and thousands of lives since 2003 to bring Iraq into its orbit, today it is Iran that appears to have achieved that goal, albeit with far less costs in terms of money and lives, observers and analysts of Iraqi affairs agree.

There appears to be no better demonstration of Iran’s success in having firmly established its hegemony across Iraq than in the current operation to retake the Sunni-dominated province of Salahuddin in central Iraq. The operation to push out Islamic State (IS) militants from Tikrit and its surrounding areas in Salahuddin is being carried out by a ragtag force of Shiite Popular Mobilization Units, the Iraqi army and some local Sunni tribes.

The largest military campaign so far against IS, the Salahuddin operation has been noted for the heavy involvement of Iranian military advisers and the conspicuous absence of the US military. While the United States has in the past aided similar operations by the Iraqi military and Popular Mobilization Units in areas such as Amerli and Baiji, no US warplanes are now dropping bombs in Salahuddin.

“The Iranians have checkmated the Americans, and I think the Americans now understand this,” Hayder al-Khoei, an Iraq expert at the London-based Chatham House, told Al-Monitor. “What’s interesting about the Salahuddin operation is that the Iraqis and the Iranians are proving to Americans: We don't need your airstrikes.”