An intelligence official told Fox News that Iran's government is fuming over the U.S. joining forces with Iraq in the fight for Tikrit -- a decision that led Iran-backed militias to stand down. 

"They are really pissed that Iraq is choosing to partner with the U.S. in the battle for Tikrit," the official said. 

The heavy involvement of Iran-backed Shiite militias in the battle for Tikrit, currently held by the Islamic State, was a big factor in the United States' initial reluctance to get involved. 

But with the U.S. launching airstrikes, Iran has threatened to order all its Shiite militias, including members of the powerful Badr Brigade, out of the area and in some cases out of Iraq, according to the official. 

"They will probably send them to Yemen," he said, referring to the widespread fighting in the unstable nation where Saudi Arabia and others are now battling Iran-backed forces for control. 

But when asked to characterize the feeling inside the Pentagon about Iran's pull-back in Tikrit, the official answered, "We are pleasantly surprised how pissed off they are." 

While the Iran-backed militias say they withdrew in protest, the Defense Department has maintained that was a precondition of U.S. involvement. 

Gen. Lloyd Austin, leader of U.S. Central Command, told members of the Senate Armed Services Committee that before airstrikes in Tikrit began, the Iraqi government agreed to preconditions stipulating the U.S. would participate as long as the Iran-backed Shiite militias withdrew from Tikrit.   

"I will not, and I hope we never, coordinate or cooperate with Shiite militias," Austin told lawmakers Thursday. 

The battle to defeat ISIS in the Sunni stronghold of Tikrit began on March 2, but stalled after three weeks, according to Pentagon officials. U.S. airstrikes against ISIS in Tikrit began Wednesday. The U.S.-led coalition announced 17 strikes by U.S. warplanes against targets in and around Tikrit. 

A spokesman for Iraq's Popular Mobilization Units, which mostly consist of Iranian-backed Shiite militias, maintained his forces were boycotting the operation on their own terms, not the Americans' terms. 

"[The U.S.] involvement is potentially harmful to the operation," militia spokesman Mouin al-Kadhimy told the Associated Press. "We are capable of liberating Tikrit without the help of American forces."

Lucas Tomlinson is the Pentagon and State Department producer for Fox News Channel. You can follow him on Twitter: @LucasFoxNews