A senior Iraqi military commander has said it will take a few days to fully dislodge al-Qaida-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 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.
US Secretary of State John Kerry said America would support Iraq in its fight against the militants - but said the US would not send troops to Iraq, calling the battle "their fight".
He told reporters the US was very concerned by the al-Qaida linked gunmen who have largely taken over Fallujah and Ramadi in an uprising that has been a blow to the Shia-led government of Iraqi prime minister Nouri al-Maliki.
The two cities are in Anbar province, a vast desert area on the borders with Syria and Jordan that was the heartland of the Sunni insurgency that rose up against American troops and the Iraqi government after the 2003 US-led invasion that toppled Saddam Hussein.
Fallujah became notorious among Americans when insurgents in 2004 killed four American security contractors and hung their burned bodies from a bridge. Ramadi and other cities have remained battlegrounds as sectarian bloodshed has mounted, with Shia militias killing Sunnis.
"We are very, very concerned about the efforts of al-Qaida and the Islamic State of Iraq in the Levant, which is affiliated with al-Qaida, who are trying to assert their authority not just in Iraq, but in Syria," Mr Kerry said before leaving to visit Jordan's King Abdullah II and Saudi Arabia's King Abdullah .
"These are the most dangerous players in that region. Their barbarism against the civilians in Ramadi and Fallujah and against Iraqi security forces is on display for everyone in the world to see."
He said the US stands with the Iraqi government and others seeking to push back militants who are trying to destabilise the region and undermine a democratic process in Iraq. He said the US was in contact with tribal leaders in Anbar who are standing up to the terrorists.
But he added: "This is a fight that belongs to the Iraqis. 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."