KIRKUK, Iraq (AFP) - Iraqi forces have retaken the Salaheddin provincial government headquarters in Tikrit from the Islamic State in Iraq and Syria (ISIS) group, a significant advance in the battle to recapture the city, officials said Tuesday.

The spokesman for the Badr militia said members of the Popular Mobilisation units - pro-government paramilitary forces dominated by Iran-backed Shi'ite militias - took part in the fighting, after some froze offensive operations last week in response to US-led air strikes.

"Iraqi forces cleared the government complex in Tikrit," an army major general said, speaking on condition of anonymity.

"The government buildings have been under our control since last night (Monday)."

It is the most significant advance in Tikrit since pro-government forces launched an operation to retake the city on March 2, their largest since ISIS led an offensive that overran much of the country's Sunni Arab heartland last June.

Salaheddin Governor Raad al-Juburi confirmed that the government headquarters had been retaken, saying that Iraqi flags now flew over various recaptured buildings in the city.

Badr spokesman Karim al-Nuri also said that the government headquarters was recaptured, and that Popular Mobilisation members fought alongside federal police in the operation.

Key Shi'ite militia forces said they were halting Tikrit operations when a US-led anti-ISIS coalition began air strikes in the area after weeks in which Iran was the main foreign partner in the operation.

The coalition strikes started last Wednesday, angering Shi'ite militiamen who accused Washington of attempting to hijack their victory.

The Pentagon conditioned its intervention on an enhanced role for regular government forces, and on Friday hailed the withdrawal from the fight of "those Shi'ite militias who are linked to, infiltrated by, (or) otherwise under the influence of Iran".

The coalition said it carried out three strikes in the Tikrit area from Sunday to Monday, in its most recent statement on the operation.

After giving themselves political cover by declaring that they do not want to work with each other, both sides are still taking part in the Tikrit operation.