Iraqi and Kurdish forces, supported by Sunni tribes and Shia armed groups, have begun to push back ISIL forces from a swathe of territory the group seized last year in their quest to build an Islamist "caliphate".

On February 13, as Al-Baghdadi was falling to ISIL fighters, suicide bombers attacked Iraqi forces protecting the Ayn al-Asad air base, where a small contingent of US troops works with Iraqi allies.

No Americans were hurt in the assault but their relative proximity to the fighting increased fears that US ground troops could find themselves drawn into the conflict.

Elaborating on the development, Al Jazeera's Arraf said "Al-Baghdadi is significant to the US because of course their troops are at the Ayn al-Asad air base, which is not far from there, and significant to Iraqis because thousands of people from the town were displaced. Some of them had to be evacuated by air by the military after ISIL surrounded the town."

Battle for Tikrit

Iraqi government troops and Shia armed groups were also likely to prevail in the unfolding battle for Tikrit, Martin Dempsey, the top US general, said on Saturday.

The US credits the coalition attacks with halting the group's territorial advances. But in the Tikrit offensive, which began on Monday, the US is on the sidelines.

"If it weren't for the [US-led coalition] air campaign over time depleting the ISIL forces in Beiji ... then the current campaign [in Tikrit] as currently constructed would not be militarily feasible," Dempsey said.

ISIL fighters had surged into Beiji, which lies just north of Tikrit, in hopes of controlling a key oil refinery there. But they have been halted and tied down by a series of US air strikes, Dempsey, who is the chairman of the joint chiefs of staff, said.

That little-noted ISIL setback has divided and weakened its forces, he said.

"The important thing about this operation in Tikrit is less about how the military aspect of it goes and more about what follows," Dempsey said.

Dempsey, who was traveling from Washington to Iraq, was asked if he believes ISIL will be pushed out of Tikrit.

"Yeah, I do," he said. "The numbers are overwhelming."

Dempsey said about 23,000 Shia fighters and Iraqi soldiers were involved in the offensive, compared to only "hundreds" of ISIL fighters.

"I wouldn't describe it as a sophisticated military manoeuvre," he said.