A senior Iraqi military commander said Sunday that it will take a few days to fully dislodge al-Qaeda-linked fighters from two key western cities.

Lt. Gen. Rasheed Fleih, who leads the Anbar Military Command, told the state television 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 only is offering 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.

Residents say it has been quiet since Saturday night in Fallujah, where militants still control the centre of the city. Sporadic clashes took place Sunday in and around Ramadi. The residents spoke on condition of anonymity for their safety.

The Islamic State in Iraq and Levant has seized control of Fallujah and Ramadi, the capital of Iraq's Anbar province. Ramadi was a stronghold of Sunni insurgents during the U.S.-led war. Al-Qaeda-linked militants largely took both cities over last week and have been fending off incursions by government forces there since.

ISIL (Islamic State of Iraq and the Levant) is also one of the strongest rebel units in Syria, where it has imposed a strict version of Islamic law in territories it holds and kidnapped and killed anyone it deems critical of its rule. Also on Saturday, it claimed responsibility for a suicide car bombing in a Shia-dominated neighbourhood 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 Shia-led government withdrew army forces from the cities. Sunni lawmakers see the army as a tool of Prime Minister Nouri al-Maliki to target his rivals and consolidate power.

U.S. will not send troops

U.S. Secretary of State John Kerry said that America would support Iraq in its combat with the al-Qaeda group, but without sending troops on ground.

The U.S. was "very, very concerned" by the fighting, Kerry told reporters as he left Jerusalem for Jordan and Saudi Arabia on Sunday to discuss his effort to broker peace between Israel and the Palestinians. However, he said the U.S. would not send ground troops in to support Iraqi forces.

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

Violence in Iraq spiked in April after the government staged a deadly crackdown on a Sunni protest camp. Iraq's al-Qaida branch has fed on Sunni discontent and on the civil war in neighbouring Syria, in which mostly Sunni rebels fight a government whose base is a Shiite offshoot sect.

Militants have targeted civilians, particularly in Shia areas of Baghdad, with waves of coordinated car bombings and other deadly attacks.

According to the United Nations, Iraq had the highest annual death toll in 2013 since the worst of the sectarian bloodletting began to subside in 2007. The UN said violence killed 8,868 last year.