TIKRIT, Iraq – Iraqi troops started the final phase of an offensive to recapture Saddam Hussein’s hometown of Tikrit on Thursday, a military official said, just hours after the United States launched airstrikes on the Islamic State-held city.

The push, however, is going ahead without the country’s Iran-backed Shiite militias, which had been instrumental to the operation so far and which backed out in protest over the U.S. action.

Late Wednesday, the U.S. began airstrikes on Tikrit at Iraq’s request and in support of the stalled ground offensive, Lt. Gen. James L. Terry, the commander of the U.S.-led campaign to defeat the Islamic State group.

He said the airstrikes would “destroy ISIL strongholds with precision, thereby saving innocent Iraqi lives while minimizing” unintended damage to civilian structures. ISIL is one of the acronyms for the Islamic State group.

A militia spokesman, Mouin al-Kadhimy, said Thursday that many of the Shiite fighters decided to boycott the Tikrit operation because of the “harmful” involvement of U.S. airstrikes.

During the day, clashes intensified as Iraqi troops and special forces moved toward the city centre, Lt. Gen. Abdul-Wahab al-Saadi told The Associated Press. An AP reporter heard a second round of airstrikes over Tikrit.

Late Thursday, Prime Minister Haider al-Abadi visited Camp Speicher military base near Tikrit to meet with military commanders and be briefed on their progress since U.S. airstrikes began.

The Islamic State group seized the Sunni city last summer during its lightning advance across northern and western Iraq. The battle for Tikrit is seen as a key step toward eventually driving the Islamic State group from Iraq’s second largest city Mosul, which is further north.

Earlier, al-Abadi said Iraqi forces began the “final phase” in the Tikrit offensive but did not acknowledge that U.S.-led coalition forces were playing a direct role. He said Iraqis, “and not anyone but you,” will claim victory against the militant group.

The U.S. first launched airstrikes to reinforce Iraq’s embattled military in August.

A spokesman for Iraq’s Popular Mobilization Units, the vast majority of which consists of Iranian-backed Shiite militias, said that a number of Shiite militias, including Asaib Ahl al-Haq, Ketaeb Hizbollah and Muqtada al-Sadr’s Peace Brigades are boycotting the Tikrit operation because of the involvement of U.S. forces.

“Their involvement is potentially harmful to the operation,” militia spokesman al-Kadhimy told the AP, adding that the powerful Badr Brigade will most likely join the boycott. “We led the fight to liberate al-Dawr, to liberate al-Alam, and we are capable of liberating Tikrit without the help of American forces.”

Iranian military advisers have been providing significant support since the Tikrit offensive began on March 2, arming and training the Iraqi Shiite militias, which have played a prominent role on the battlefield. Militiamen make up more than two-thirds of the force fighting the Islamic State group in Tikrit.

But the top U.S. general for the Middle East said Thursday that Iranian forces and Shiite militia have left the fight and pulled back from Tikrit as a condition to U.S. involvement. Gen. Lloyd Austin told the Senate Armed Services Committee that the U.S. agreed to come in with airstrikes under the condition that the militias pull back.

Austin, who heads U.S. Central Command, said that there now are about 4,000 Iraqi forces, commandos and police battling for the city, and with American help, he believes the campaign to retake the city will move forward.

The Combined Joint Task Force-Operation Inherent Resolve said in a statement that coalition forces conducted 17 airstrikes approved by the Iraqi Ministry of Defence, hitting targets including an IS building, two IS bridges, three IS checkpoints, an IS roadblock and an IS controlled command and control facility.