Security officials and tribal leaders have said Prime Minister Nouri al Maliki agreed to hold off an offensive to give people in Falluja time to push the militants out. But it is not clear how long they have before troops storm the town, close to Baghdad, where US forces fought notable battles a decade ago.
Fighters, some of them foreign, from the Islamic State of Iraq and the Levant (ISIL), an al Qaeda affiliate also active across the border in Syria, overran police stations in Falluja and another city in Iraq's western Anbar province last week.
Many in Iraq's once dominant Sunni Muslim minority, the main group in Anbar, share ISIL's dislike of Maliki's Shi'ite-led government. But tribal leaders in the province are trying to steer a path between the army and the al Qaeda fighters.
One Sunni tribal leader in Falluja said: "If the army attacks Falluja to fight a handful of al Qaeda elements, that will have dire consequences by triggering endless violence.
"We are sending a clear message to the government. Go ahead and fight al Qaeda outside Falluja and we ourselves will deal with the issue inside the city."
Iraq's US-equipped armed forces have already shelled and launched airstrikes against militants over the past week.
Officials say dozens of militants have been killed, but the number of casualties among civilians, security forces and tribal fighters is not yet clear.
The violence has underlined how civil war in Syria has inflamed a broader confrontation across the Middle East between Shi'ite Iran, the main ally of President Bashar al Assad, and Sunni powers like Saudi Arabia, which back the Syrian rebels.
The US has said it would speed up deliveries of military hardware, including drones and missiles, to Iraq. It has ruled out sending back troops, two years after Washington ended nine years of occupation.
ISIL has for some months been tightening its grip on Anbar, with the stated aim of creating a Sunni religious state straddling the border into Syria's rebel-held eastern desert provinces.
Iraqi security forces backed by tribal fighters regained control in the centre of Anbar's provincial capital Ramadi on Monday, a special forces officer said. Fighting continued in some areas yesterday while in the centre, government offices, hospitals and markets reopened.
US Vice-President Joe Biden spoke with Mr Maliki on Monday night to express support for Iraq's fight against al Qaeda-linked militants, a message Mr Biden repeated in another call on Monday with Osama al Nujaifi, speaker of the Iraqi Council of Representatives.
The White House said Mr Biden, in his call with Mr Nujaifi, praised the recent cooperation between Iraqi Security Forces and Sunni local, tribal, and national leaders in the fight against ISIL.
The US is looking to provide additional shipments of Hellfire missiles to Iraq as early as this spring as well as 10 ScanEagle surveillance unmanned aerial vehicles (UAVs) in forthcoming weeks and 48 Raven surveillance UAVs later this year to help Iraq track insurgent groups.
Washington also delivered three Bell IA-407 helicopters to Iraq in December, bringing total helicopter sales and deliveries to the country to 30.
Meanwhile, at least four people were killed in bomb attacks in Iraq yesterday. A suicide bomber rammed a truck into a police station in the northern city of Kirkuk, killing two people, and two died in roadside bomb attacks south-east of Baghdad.