An operation is under way to drive hardline fighters out of Iraq's Anbar province, with an aerial assault by government forces hitting east of Fallujah, and clashes between the Iraqi army and al-Qaeda-linked Islamic State of Iraq and the Levant (ISIL) near Ramadi leaving many dead.

Iraqi officials said fighting between the army and al-Qaeda-linked rebels near the provincial capital of Ramadi left at least 34 people dead on Sunday, including 22 soldiers and 12 civilians, AP news agency reported.

The officials also said 58 people were wounded in the clashes, along with an unknown number of anti-government fighters.

We are not obviously contemplating returning, we are not contemplating putting boots on the ground, this is their fight. John Kerry,

US secretary of state

Iraq's Defence Ministry also released footage on Sunday that it said showed aerial bombings of al-Qaeda fighters' hideouts, after the government vowed earlier in the day to launch a "major attack" to retake Fallujah.

The city has been in the hands of fighters from ISIL since Saturday, a senior security official said.

Iraqi officials said on Sunday that it would take a few days to wrestle Fallujah and Ramadi from ISIL control.

Some local Sunni tribes insisted they should be included in any military operation, while other tribes in the area vowed to fight government forces attempting to take action in the area.

"The tribal revolutionaries will fight to protect the city of Fallujah and we swear to take on anyone from this sectarian government. And we also promise to repel this dirty act by the central government," an unnamed commander of the Fallujah Military Council said.

The takeover of Fallujah and parts of Ramadi, farther west, is the first time that tribal fighters have exercised such open control in major cities since the height of the bloody insurgency that followed the US-led invasion of 2003.

US 'very concerned'

US Secretary of State John Kerry said on Sunday that the United States would provide assistance to Iraqi forces in their battle against the group but that it was "their fight".

Kerry said Washington was "very, very concerned" about the resurgence of ISIL but said it was not contemplating any return of US ground troops, after their withdrawal in December 2011.

"We are not obviously contemplating returning, we are not contemplating putting boots on the ground, this is their fight," Kerry told reporters in Jerusalem.

"But we're going to help them in their fight... We are going to do everything that is possible to help them."

On Friday and Saturday, more than 160 people were killed in the worst violence to hit Anbar province in years.

Al Jazeera's Iraq correspondent, Imran Khan, said: "For a lot of Iraqis... they don't want the return to US boots on the ground because they feel that that's just going backwards. But what they would like is much more public support from the Americans, and they'd also like much more military hardware support from the Americans."

Baghdad bombings

Elsewhere in Iraq, a wave of bombings earlier on Sunday hit the capital, Baghdad, killing at least 20 and wounding dozens more, Iraqi authorities said.

Iraqi police said the deadliest in Sunday's attacks took place in Baghdad's northern Shaab neighbourhood, when two parked car bombs exploded simultaneously near a restaurant and a tea house. Officials said that blast killed at least ten people and wounded 26.