Sunni fighters take up position in Fallujah city, western Iraq, 05 January 2014. According to media reports, militants from the Islamist State in Iraq and
Sunni fighters take up position in Fallujah city, western Iraq, 05 January 2014. According to media reports, militants from the Islamist State in Iraq and the Levant (ISIL) have taken full control of Iraq's city of Fallujah and large areas of Ramadi, two key cities in the western province of Anbar, after government forces cleared out an anti-government Sunni protest camp. EPA/MOHAMMED JALIL

BAGHDAD — The Iraqi military tried to dislodge al-Qaeda militants in Sunni-dominated Anbar province Sunday, unleashing airstrikes and besieging the regional capital in fighting that killed at least 34 people, officials said.

The recent gains by the insurgents have been a blow to the Shiite-led government — as sectarian violence has escalated since the U.S. withdrawal. U.S. Secretary of State John Kerry said Washington was "very, very concerned" by the fighting but would not send in American troops.

"This is a fight that belongs to the Iraqis," Kerry said. "That is exactly what the president and the world decided some time ago when we left Iraq, so we are not obviously contemplating returning. We are not contemplating putting boots on the ground. This is their fight. ... We will help them in their fight, but this fight, in the end, they will have to win, and I am confident they can."

The U.S. recently supplied Iraq with Hellfire missiles used against militants.

Video of the airstrikes in Anbar — apparently taken by aircraft at night — was released by Iraq's Defense Ministry, showing al-Qaeda hideouts being bombarded. It showed men gathered around a vehicle, then running away as the site was struck.

A ministry statement said the air force struck a militants' hideout overnight, identifying them as belonging to the al-Qaeda-linked Islamic State in Iraq and the Levant, which the government refers to as "terrorists."

The army and allied tribesmen also fought al-Qaeda militants around the provincial capital of Ramadi on Sunday, two Anbar government officials said by telephone. They said 22 soldiers and 12 civilians were killed, along with an unknown number of militants, and 58 people were wounded. The officials spoke on condition of anonymity because they were not authorized to brief reporters.

Clans inside the city of Fallujah have started to form brigades, they said, and some of the factions who fought the Americans after the U.S.-led invasion a decade ago say they do not want the Iraqi army to enter the city. There was no fighting inside the city Sunday.

Government troops, backed by Sunni tribesmen who oppose al-Qaeda, have encircled Fallujah for several days and have entered parts of Ramadi. On Friday, troops bombarded militant positions outside Fallujah with artillery, a military official said, speaking on condition of anonymity because he was not authorized to release information.

Earlier on Sunday, a senior Iraqi military commander said that it will take a few days to fully dislodge al-Qaeda-linked fighters in the two cities.

Lt. Gen. Rasheed Fleih, who leads the Anbar Military Command, told state TV Sunday that "two to three days" are needed to push the militants out of Fallujah and parts of Ramadi. Fleih added that pro-government Sunni tribes are leading the operations, while the army is offering only aerial cover and logistics on the ground. He didn't elaborate on the operations.

"The quiet and safe life that is sought by the Anbaris will not be completely restored before few hours or two to three days, God willing," Fleih said.

Ramadi was a stronghold of Sunni insurgents during the U.S. war. Al-Qaeda militants largely took both cities over the last week and have been fending off incursions by government forces there since.

ISIL is also one of the strongest rebel units in neighboring Syria, where it has imposed a strict version of Islamic law in territories it holds in the civil war raging there. It also has kidnapped and killed dozens of people it deems critical of its rule. On Saturday, it claimed responsibility for a suicide car bombing in a Shiite-dominated neighborhood in Lebanon.

Tensions in Anbar have run high since Dec. 28, when Iraqi security forces arrested a Sunni lawmaker sought for terrorism charges. Two days later, the government dismantled a months-old, anti-government Sunni protest camp, sparking clashes with militants.

To ease the tension, the government of Prime Minister Nouri al-Maliki withdrew army forces from the cities. Sunni lawmakers see the army as a tool of al-Maliki to target his rivals and consolidate power.

Violence in Iraq spiked in April after the government staged a crackdown on a major Sunni protest camp. Iraq's al-Qaeda branch has fed on Sunni discontent and on the civil war in neighboring Syria.