A car carrying explosives ripped into a U.S. convoy Wednesday in northern Iraq, killing at least 10 people, and U.S. troops encountered pockets of resistance in Fallujah, a city wrecked by more than a week of fighting.

Black smoke billowed over Fallujah, once home to about 250,000 people, as insurgents staged hit-and-run raids on U.S. patrols moving through the city's dense warrens. Military commanders said they had no estimates on the number of rebels still fighting, but the staccato bursts of gunfire and thunder from tank rounds in the city's center countered Iraqi and U.S. claims over the weekend that the battle there had largely ended.

U.S. commanders said they held the entire city but acknowledged that rebels have moved back into areas that were believed to have been secured. While the entrances to the city are blocked, the insurgents may be plying old paths into Fallujah or crossing the Euphrates River, whose palm-shrouded banks skirt the city.

In Baiji, an oil refinery town north of Baghdad, the U.S. military said a car carrying explosives barreled toward a Bradley Fighting Vehicle and detonated, wounding three soldiers. The military did not say how many civilian casualties there were, but news agencies, quoting hospital officials, reported that at least 10 people were killed in the blast and the shooting that ensued.

Insurgents in Baiji, a town that has long been unstable, have tried to target the oil refinery and other installations and establish a greater presence in the streets.

In Mosul, which more than 2,500 U.S. troops entered Tuesday after attacks by insurgents on police stations, four of the city's five bridges spanning the Tigris River remained closed. But residents reported the streets were quieter, and fewer rebels were seen in public.

Since last week, fighting has surged across a swath of Iraq stretching from northern cities to a turbulent area south of Baghdad, where residents say Sunni Muslims intent on strict religious rule have almost complete control such towns as Latifiyah and Mahmudiyah.

The fighting, which has killed dozens of U.S. troops and hundreds of insurgents, has played out as efforts continue to prepare Iraq for elections at the end of January. The American military is determined to achieve at least a modicum of stability, particularly in the restive Sunni regions. Insurgents are no less determined to derail the voting, which, if successful, would probably be perceived as a victory for the U.S. project in Iraq.

The insurgents' tactics have ranged from more conventional guerrilla warfare, with the daily deployment of car bombs, to the sabotage of Iraq's tattered oil pipelines and other infrastructure to the brutal intimidation of Iraqi police, National Guard and army units whose development U.S. officials have made a priority.

The Interior Ministry said Wednesday that it was investigating a report from police in the southern city of Karbala that 31 recruits may have been abducted in Rutbah, in the west, as they returned from training in neighboring Jordan. But a spokesman, Sabah Kadhim, said the ministry had no information about any kidnappings and said the police chief in Rutbah, contacted Wednesday night, had no report of abductions.

"I cannot confirm anything," Kadhim said. "There are a lot of rumors right now."

In past months, insurgents have kidnapped security force recruits and their relatives, and on Monday, the Interior Ministry reported that a wounded policeman had been seized from his hospital bed and dismembered, his remains hung in a city square. In October, gunmen ambushed a group of unarmed army recruits returning home from training. Forty-nine of them were killed execution-style, with gunshots to the back of the head.

Along a street in Baghdad, next to banners of the most feared insurgent group, now known as al Qaeda in Iraq, guerrillas have strung up uniforms of Iraqi National Guard members as a warning.

In Fallujah, which was a base for the insurgent group, fighting flared again Wednesday, with a near-constant barrage of mortar and rifle fire. In a neighborhood in the eastern part of the city, snipers penetrated a building held by Marines. A rocket barrage forced a reporter to leave the scene, and it was unclear how the clash ended.

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.