RAMADI - Iraqi Prime Minister Nuri al-Maliki called on Fallujah residents to expel "terrorists" to avoid a security forces assault, as the United States said it would speed up deliveries of missiles and surveillance drones to the Baghdad government.
Fallujah has been outside government control for days, while parts of Anbar provincial capital Ramadi, farther west, are also held by militants.
It is the first time militants have exercised such open control in major cities since the height of the bloody insurgency that followed the US-led invasion of 2003.
Maliki called on "the people of Fallujah and its tribes to expel the terrorists" so "their areas are not subjected to the danger of armed clashes," state television reported.
He also ordered security forces "not to strike residential areas in Fallujah".
A senior official told AFP on Sunday that Iraqi forces were preparing a major attack on Fallujah.
And ground forces commander Staff General Ali Ghaidan Majeed said the city should "wait for what is coming" - a reference to an impending assault.
Sheikh Ali al-Hammad, a senior tribal leader from Fallujah, insisted on Monday that Al-Qaeda-linked Islamic State of Iraq and the Levant (ISIL) forces had departed the city, saying it is now held by Sunni tribesmen.
"There is no ISIL in the city," Hammad told AFP by telephone. "They all left."
"The gunmen inside are from the sons of the tribes, and they are here to defend" Fallujah, he said.
A witness said ISIL fighters were still in the city, but had lowered their characteristic black flags to avoid being targeted, and Iraqi officials had previously said ISIL was in control.
However, Fallujah remains outside government control and even if the departure of ISIL militants is confirmed, Baghdad may still seek to retake it.