The head of a powerful Shiite militia on Sunday criticised "weaklings" in the Iraqi army who want US-led air strikes to support the massive operation to retake Tikrit from jihadists.

The remarks by Hadi al-Ameri point to a possible divide between the Iraqi army and allied paramilitaries known as "Popular Mobilisation" units, which are dominated by Shiite militia forces, over the now-stalled Tikrit drive.

"Some of the weaklings in the army... say we need the Americans, while we say we do not need the Americans," Ameri told journalists at Camp Ashraf, north of Baghdad, when asked about US-led air support for Tikrit.

Army Staff Lieutenant General Abdulwahab al-Saadi, a top commander in Salaheddin province, of which Tikrit is the capital, told AFP that he had requested such strikes against the Islamic State jihadist group and that they were needed.

But the Pentagon said that the Iraqi government has not made any request for air support for the Tikrit operation, which began on March 2.

Forces from the army, the police and a number of different militias are taking part in the operation, bringing different tactics, skill levels and willingness to take casualties to the fight.

It is unclear who if anyone has overall command of the operation, and disputes between the forces involved would hamper an effort that has already become bogged down by the huge number of bombs planted by IS in the city's streets and houses.

While pro-government forces were able to take control of towns near Tikrit and then surround it, fighting to clear the city itself proved much more difficult, and the operation has been halted and the IS fighters besieged.