U.S. jets pounded insurgent positions in Fallujah (search) for a second straight day Wednesday, raising plumes of smoke but leaving no extensive damage or signs of weakening the Sunni militants (search) who have steadily expanded their control of this city about 30 miles west of Baghdad.

After the attacks, bands of fighters, many wearing loose black pajama-like pants and T-shirts, lounged outside abandoned buildings facing the American lines, seeking to escape the intense sunlight of a day when temperatures topped 114 degrees.

Most hid their faces with Arab head scarves or ski masks. Some quenched their thirst with water from coolers beside them. Most appeared to be in their late teens or early 20s and 30s, but a few looked as old as 50.

Elsewhere in this city of 300,000, fighters patrolled the streets in new American pickups. One resident, 33-year-old Abu Rihab, said they were part of a 16-vehicle fleet commandeered between Jordan and Baghdad.

The Fallujah Brigade (search), which the Americans organized in May to maintain security after the Marines lifted a three-week siege, has all but disappeared, along with virtually all signs of Iraqi state authority.

Members of the Iraqi national guard, which was supposed to back up the Fallujah Brigade, fled the city after one of their commanders was executed by insurgents for allegedly spying for the Americans. Local police operate under the tacit control of the militants.

The airstrikes, in the eastern and southern parts of this city, targeted a militant "command and control headquarters" that has been coordinating attacks against U.S. and Iraqi forces, the U.S. military said in a statement.

"Initial assessments indicate there are no noncombatant casualties," the U.S. statement added. "Enemy casualty figures cannot be confirmed."

Hospital officials said two people were killed in the attack but did not say whether they were insurgents. Late Tuesday, U.S. jets dropped several bombs and tank and artillery units fired rounds into Fallujah in retaliation for militant attacks on Marine positions outside the city, said Marine spokesman Lt. Col. T.V. Johnson.

Despite the formal end of the U.S. occupation on June 28, the interim Iraqi government has lost control over key Sunni Muslim cities such as Fallujah, Ramadi and Samarra. The commander of the U.S. 1st Infantry Division said his troops and their Iraqi allies would regain control of Samarra before Iraq's general election expected in January.

Maj. Gen. John Batiste said he was confident that a combination of diplomacy, U.S. aid and Army intimidation would persuade the city's 500 insurgents to give up. Otherwise, he said, the Americans would use force.

However, Gen. Richard Myers, chairman of the Joint Chiefs of Staff, acknowledged that it could be months before U.S. and Iraqi authorities are prepared to take those cities back.

"Part of that strategy is that Iraqi security forces must be properly equipped, trained and led to participate in these security operations, and then once it's over, can sustain the peace in a given city," Myers told Pentagon reporters Tuesday.

That appeared to be a tacit acknowledgment that even if the Americans regained the cities by force, the Iraqis would not be able to control them.

In Fallujah, real power is in the hands of the "Mujahedeen Shura Council," a six-member body led by Sheik Abdullah al-Janabi, spiritual leader of the militants and the undisputed ruler of the city since May.

The mujahedeen run their own courts that try people suspected of spying for the Americans or other offenses. Abu Rihab said that since May, they have put to death about 30 people convicted of spying. It was impossible to confirm the figure.

Abu Rihab said those killed had confessed to the charges and that he had personally taken part in some of the interrogations. A laser disc making the rounds in Fallujah and elsewhere shows an Egyptian man confessing to spying for the Americans along with the scene of his subsequent beheading.

Among those put to death by the mujahedeen was Lt. Col. Suleiman Hamad al-Marawi of the Iraqi national guard. After al-Marawi was killed for allegedly spying for the Americans, the entire national guard contingent, estimated to number several hundred, fled the city.

Insurgents also control most roads in and out of the city. The Fallujah Brigade has for all practical purposes ceased to function as a security force. Its members, most of whom live in Fallujah, received two months of back salary on Wednesday.

But their commander, Maj. Gen. Abdullah Hussein, says the U.S. military has refused to deal with him since Sept. 1.

Contacts are under way between Fallujah representatives and the interim government of Prime Minister Ayad Allawi. The Fallujah residents want the U.S. attacks to stop and the Americans to pay compensation to people killed in attacks.

Allawi wants city fathers to hand over Al Qaeda-linked terrorists that he and the Americans say are in Fallujah. The contacts have produced no agreements.

In other developments Wednesday:

— In eastern Baghdad, insurgents detonated a roadside bomb that killed one U.S. soldier and wounded two others, pushing the number of American military deaths in the Iraq campaign to 1,005. President Bush said "we mourn every loss of life" and declared that the United States was making good progress in the war against terrorism.

— Gunmen kidnapped the deputy governor of Anbar province, which includes Fallujah, in the latest assault on officials connected to Iraq's interim government, the Interior Ministry said.

— A U.S. military helicopter crashed west of Baghdad, but all four personnel aboard survived. A terse statement from the U.S. Marine base at Camp Fallujah gave no precise location, no time of the crash and did not say what type of helicopter was involved or whether it was downed by hostile fire.