A senior Iraqi military commander has said it will take a few days to fully dislodge al-Qa'ida-linked fighters from two key western cities.
Lt Gen Rasheed Fleih, who leads the Anbar Military Command, told state television that "two to three days" are needed to push the militants out of Fallujah and parts of Ramadi.
Lt Gen Fleih said pro-government Sunni tribes are leading the operations while the army is offering aerial cover and logistics on the ground.
Fighting has raged in Iraq's western Anbar province since Monday, with troops from the Islamic State in Iraq and the Levant (ISIL) taking over the centre of Fallujah and some parts of Ramadi.
Residents say it has been quiet in Fallujah since Saturday night, while sporadic clashes took place in Ramadi.
The ISIL, an insurgent group active in Iraq and Syria, has seized control of Fallujah and Ramadi, the capital of Iraq's Anbar province. Ramadi was a stronghold of Sunni insurgents during the US-led war. Al-Qai'da militants largely took both cities over last week and have been fending off incursions by government forces since then.
The ISIL 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.
Tensions in Anbar have been running high since 28 December, 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.
The US Secretary of State, John Kerry, has said that America would support Iraq in its combat with al-Qa'ida, but without putting troops on the ground.
The US was “very, very concerned” by the fighting, Kerry told reporters as he left Jerusalem for Jordan and Saudi Arabia to discuss his effort to broker peace between Israel and the Palestinians. However, he said the US would not send ground troops in to support Iraqi forces.
Violence in Iraq spiked in April after the government staged a deadly crackdown on a Sunni protest camp. Iraq's al-Qa'ida branch has fed on Sunni discontent and on the civil war in neighbouring Syria.
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.