BAGHDAD — The Iraqi army deployed tanks and artillery around Fallujah Tuesday, security officials said, as local leaders in the besieged city urged al-Qaida-linked militants to leave in order to avert an impending military assault.

Security officials and tribal leaders have said that 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 U.S. forces fought notable battles a decade ago.

Fighters, some of them foreign, from the Islamic State of Iraq and the Levant (ISIL), an al-Qaida 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 Shiite-led government. But tribal leaders in the province are trying to steer a path between the army and the al-Qaida fighters.

"If the army attacks Fallujah to fight a handful of al-Qaida elements, that will have dire consequences by triggering endless violence," one Sunni tribal leader in Fallujah told Reuters, adding that it could spread to other Sunni districts.

"We are sending a clear message to the government," he said. "Go ahead and fight al Qaeda outside Falluja and we ourselves will deal with the issue inside the city."

Iraq's U.S.-equipped armed forces have already shelled and launched airstrikes against militants over the past week. Sunni tribesmen from the area are fighting on both sides.

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 Shiite Iran, the main ally of President Bashar Assad, and Sunni powers like Saudi Arabia, which back the Syrian rebels.

The United States said on Monday that 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, a thinly populated region the size of England, 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 on Tuesday, he added.

In the center, government offices, hospitals, and markets reopened.