Iranian forces and Shia militia groups have pulled back from front line around Tikrit, as US airstrikes were launched to help Iraqi forces battling Islamic state of Iraq and the Levant (ISIL), a top US general has said.

General Lloyd Austin, the head of US Central Command, told the Senate Armed Services Committee on Thursday that the US agreed to come in with air strikes in Tikrit under the condition that the militias pull back.

I will not, and I hope we never, coordinate or cooperate with Shia militias Lloyd Austin, the head of US Central Command

The US General told the committee that he had insisted that Iranian-backed militias pull back before the US began flying intelligence-gathering flights over the weekend and dropping bombs on Wednesday.

"I will not, and I hope we never, coordinate or cooperate with Shia militias," he told the Committee.

The US general said that the campaign being waged by Iranian-back militias working with Iraqis had stalled. The ISIL group seized the Sunni city, Saddam Hussein's hometown, last year during its rapid advance across northern Iraq.

Austin said that the Iraqi government accepted as a condition of US airstrikes that Shia militias will not be part of the effort to stabilise the city once it is recaptured, the AP news agency reported.

However, spokespersons for a number of the militias rejected Austin's claim, saying they chose to withdraw from the battle for Tirkit in protest of the US entering the fray.

The Kataib Hizbollah and Asaib Ahl al-Haq militias both suspended their participation in Tikrit on Thursday , although the Badr Organisation, which is the largest and most powerful group within the Hashid Shaabi, said it would continue to fight.

It is not possible for Kataib Hizbollah or any of the resistance factions to be in the same trench as the Americans Jaafar al-Husseini, Military spokesman for Kataib Hizbollah

'Came to usurp our victory'

The US-led coalition joined the fray in Tikrit at the request of Iraqi military commanders, but Shia militia commanders publicly rejected any US role in the campaign to retake the ISIL bastion.

"We were able to conclude the battle ourselves, but the US came in order to usurp this major victory," Asaib Ahl al-Haq spokesman Naim al-Uboudi said.

Jaafar al-Husseini, a military spokesman for Kataib Hizbollah, criticised Prime Minister Haider al-Abadi for inviting the coalition to join the battle for Tikrit.

Speaking at an airbase where Iraqi planes were taking off to fly sorties over Tikrit, Iraq's Defence Minister Khaled al-Obeidi played down the role of Iranian advisers in the battle, the Reuters news agency reported.

"The Iranian advisers have nothing to do with the work of the air force," Obeidi said.

"The Iranians are working with the brothers in the Hashid Shaabi as advisers, and I think their presence is always in the rear positions."