Just outside the city, U.S. warplanes bombed a suspected hideout after insurgents tried to attack a passing convoy. Dust thrown up by the blast could be seen a mile away.
Residents said fighters were fleeing south, some of them swimming across the Euphrates with their weapons. One 32-year-old guerrilla, who identified himself as Abu Salman, said the attacks in that part of the city were intended to divert U.S. attention and allow others to escape.
The corpses of slain fighters could still be seen in the streets, and more than 100 rebels, dozens of them Arabs from outside Iraq, were buried in a new graveyard. Residents said a statement purportedly from Abu Musab Zarqawi, the Jordanian militant who leads al Qaeda in Iraq, was circulated among those still fighting, urging them to take their campaign to Baghdad and target the Iraqi police, army and foreigners.
Some of Fallujah's rebels may also have fled west to Ramadi and south to Latifiyah and nearby towns. Residents quoted by the Associated Press said that masked men with rocket-propelled grenades took up positions in neighborhoods of Ramadi, where the U.S. military has noted a more sophisticated and better-organized guerrilla presence.
The fighting in Fallujah and the eruption of clashes elsewhere in the region north and west of the capital, popularly known as the Sunni Triangle, represent tactical moves, but they also have increasingly taken on the veneer of a public relations battle. Both sides have sought to channel sentiments in a country beset by unease and fear over the worsening bloodshed.
So far, the anger unleashed by the fighting has not approached the intensity of that produced by another round of fighting in April, and regions dominated by Shiite Muslims have stayed relatively quiet.
But there are still signs of displeasure over the fighting, particularly in other Arab countries. On Rotana, a popular Arabic music channel, text messages sent by viewers and broadcast at the bottom of the screen have conveyed pledges of support for Fallujah.
"Long live Fallujah, long live the resistance," one said this week.
Staff writer Jackie Spinner in Fallujah and special correspondents Naseer Nouri and Bassam Sebti contributed to this report.