The agreement would lead to the creation of a local force of some 1,100 members called the Fallujah Protective Army that would patrol the city under the command of an Iraqi general from Saddam Hussein's military. U.S. Marines would pull out of the city.
A Marine officer in Iraq said Thursday that a deal was reached in principle but "fine points" needed to be fixed.
Deputy Defense Secretary Paul Wolfowitz, however, said there was no deal yet and officials were "still working on it."
Negotiations were also taking place in the southern city of Najaf, where tribal leaders and police discussed a proposal to end a standoff between soldiers and militiamen loyal to radical Shiite cleric Muqtada al-Sadr.
In other developments:
The commander of the proposed Fallujah Protective Army met with tribal leaders in a Fallujah mosque earlier Friday. Major Gen. Jassim Mohammed Saleh, a veteran of Saddam Hussein's Republican Guard, wore his uniform from the former Iraqi military bearing his general's insignia. One member of his entourage was seen waving an Iraqi flag from his car, reports CBS News' Lisa Barron.
Capt. Ziad Khalas of the Iraqi security forces said Iraqi police and paramilitary forces expected to enter the city later Friday.
In an apparent move to help the Fallujah negotiations, U.S. authorities Thursday released the imam of the city's main mosque, Sheik Jamal Shaker Nazzal, an outspoken opponent of the U.S. occupation who was arrested in October.
One possible sticking point in the talks could be a U.S. demand for insurgents to turn over those responsible for the March 31 killing and mutilation of four American contract workers, whose bodies were burned and dragged through the streets. Winning assurances that the perpetrators would be turned over remains a U.S. goal of the Fallujah talks.
At the main checkpoint into the city, some 200 families waited as Marines cleared coils of razor wire that blocked the road.
A U.S. Marine said engineers would later move large cement blocks that blocked the road.
One of three battalions of U.S. Marines mostly departed its positions in an industrial zone in the southern portion of the city, witnesses said.
Marines in that area began packing up their gear Thursday in preparation for a withdrawal. They also broke down earthen berms and other security barriers. But the timing of a pullback is likely to depend on talks Friday between U.S. commanders and Fallujah representatives.
Despite the negotiations, skirmishes continued between Marines and guerrillas.
Three F/A-18 Hornets flying off the aircraft carrier USS George Washington in the Gulf dropped three 500-pound bombs Thursday on targets in the Fallujah area, Navy spokesman Lt. Cmdr. Danny Hernandez said.
Witnesses reported rockets fired into the Golan neighborhood, a bastion of the insurgency, and two houses were on fire. Marines and guerrillas have clashed repeatedly in the northern district since Monday.
The Fallujah force is expected to include former Iraqi police and soldiers including gunmen who fought against the Americans, particularly ex-soldiers disgruntled over losing their jobs when the United States disbanded the old Iraqi army.
But the new force would not include "hardcore" insurgents or Islamic militants holed up in the city, a Marine officer said, speaking on condition of anonymity. Many of the guerrillas in Fallujah are believed to be former members of Saddam's regime or military.
Washington is under intense international pressure to find a peaceful solution to the standoff that has killed hundreds of Iraqis and became a symbol of anti-U.S. resistance in Iraq, fueling violence that made April the deadliest month for American forces.
U.S. Marines encircled the city of 200,000 on April 5. Hospital officials said more than 600 Iraqis, many of them civilians, were killed in the fighting along with eight U.S. Marines. But the figures were disputed by Iraq's health ministry and an exact toll was not known.