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.

Saadi was not available for comment on Ameri's remarks.

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

Ameri indirectly referenced an additional possible obstacle to US support aside from the lack of an official request: the role of Iran.

Washington may be reluctant to be directly involved in an operation in which rival Iran has been playing a major role.

"Qassem Suleimani is here whenever we need him," said Ameri, referring to Iran's top officer responsible for foreign operations.

"He was giving very good advice. The battle ended now, and he returned to his operations headquarters," he said, apparently referring to the current halt in the fight for Tikrit.

- Tikrit bombardment ongoing -

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

The latter groups are mostly composed of Shiite fighters, some in pre-existing militias while others fight for those formed since IS led a major offensive that overran large areas north and west of Baghdad last June.

Baghdad turned to militiamen to bolster its flagging forces, and they have played a role in driving IS back. But depending on them also risks further entrenching these forces, some of which have been accused of human rights violations.

It is unclear who if anyone has overall command of the Tikrit 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.

Ameri said Sunday that bombardment of the city is ongoing, and that "we will not enter Tikrit until after the completion of the necessary preparations," which relate to equipment, not personnel.

Iraqi officials have repeatedly said that the halt to the Tikrit operation is due to a desire to limit casualties among security forces and civilians, as well as damage to buildings and infrastructure.