BAGHDAD, Dec. 17 -- Iraqi authorities said residents would begin returning to Fallujah within the next week, even as U.S. forces shelled a section of the city and insurgents proclaimed they would press the fight there, more than a month after American commanders declared the city "liberated."
Mayor Mahmoud Ibrahim Jirisi said families could start returning to some southern neighborhoods of the shattered city as early as Friday, though the Reuters news agency reported that there was no sign of such movement by late afternoon.

A man pours water to prevent the spread of fire from a burning tanker in Baghdad. Witnesses said the tanker caught fire as U.S. troops battled insurgents.
(Asa'ad Muhsen -- AP)
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"U.S. forces will allow families to return to the Andalous area starting today under a 10-day timetable," Jirisi said, naming a southwest residential section of the largely empty city that was once home to about 250,000 people.
Iraq's interim government has pledged $600 to each returning family and begun positioning food and other relief materials, but it was not clear whether the city was habitable.
Fallujah has no power or water, and Marine civil affairs teams assessing damage from the massive offensive by U.S. and Iraqi troops have concluded that "extensive repair is required before reactivating the electrical grid and city water system," the military said in a statement.
The city's medical facilities are not ready either, the Marines concluded.
Fighting continues in the city. Marine officers and an insurgent spokesman said firefights have flared in houses abandoned by residents, searched and marked as "cleared" by U.S. or Iraqi forces, and then stealthily reoccupied by guerrillas.
The insurgents are sneaking through the deserted city and taking up ambush positions in the houses. An insurgent said the fighters' military goal was to cause casualties among U.S. and Iraqi patrols before dying in the fusillade the guerrillas know will come in response.
"They wish to die in Fallujah," said Abu Assad Dulaimy, a spokesman for the insurgent-led mujaheddin shura council that controlled Fallujah for six months before the U.S. and Iraqi offensive that began on Nov. 8.
"Until now, they do not control the city. Casey and Allawi said people could go back next week," Dulaimy said, referring to Army Gen. George Casey, the top U.S. commander in Iraq, and interim Prime Minister Ayad Allawi. "We will thwart that with attacks."
Senior Iraqi officials and U.S. officers describe the persistent fighting in Fallujah as little more than a nuisance militarily.
The November offensive, they say, deprived insurgents and their allies of a major command-and-control center.
A frequently stated reason for the offensive, in which more than 70 U.S. service members died, was returning the city to Baghdad's control in time for residents to take part in scheduled Jan. 30 elections.
Achieving that goal appears unlikely, with at least 200,000 Fallujans still living in makeshift camps or with relatives in other cities and voter registration officially closed.