FALLUJAH, Iraq – American troops, on the verge of gaining control of the city, fought pockets of resistance in this former terrorist stronghold yesterday and uncovered what the Iraqi commander said were “hostage slaughterhouses” in which foreign captives had been killed.

Terrorists sought to open a second front, mounting attacks outside Fallujah and kidnapping three relatives of Prime Minister Allawi. Terrorists also claimed to have abducted 20 Iraqi National Guard troops in Fallujah.

Throughout the day, Americans hit the terrorists with artillery and mortars, and warplanes fired on the city’s main street and market as well as Jolan, one of several neighborhoods where troops were skirmishing with terrorists.

In what could be a sign of progress, the Marines began turning over Jolan to Iraqi forces, signaling that Marines consider the area relatively secure. Jolan was considered one of the strongest positions held by terrorists inside Fallujah.

Even so, an Associated Press reporter embedded with them witnessed continued clashes in Jolan and smoke billowing from the heart of the neighborhood late last night. Fireballs and tracer fire lit up the night sky over Fallujah and the sounds of artillery echoed in the streets.

In one of the most dramatic clashes of the day, snipers fired on American and Iraqi troops from the minarets of the Khulafah Al Rashid mosque, the military said. Marines said the terrorists waved a white flag at one stage but then opened fire, BBC’s embedded correspondent Paul Wood reported. The troops called in four precision air strikes that destroyed the minarets but left the mosque standing.

Pool footage showed American forces battling insurgents in a neighborhood surrounding the mosque. Troops were pinned down by gunfire on a rooftop, forced to hit the deck, and lay on their stomachs.

“We’re taking fire from the mosque,” one of the Americans said. Forces returned fire, blasting the mosque – a large domed building flanked by two minarets – and sending up clouds of debris.

“When they’re using a mosque to do command and control for insurgents and kill my fellow Marines, and soldiers, and airmen that are out here – no holds barred, the gloves are off,” said Marine Staff Sergeant Sam Mortimer.

Tank gunners also opened fire on terrorists in a nearby five-story apartment building, and flames shot from several windows.

The top American commander in Iraq, General George Casey, told President Bush yesterday that his troops were “making very good progress” securing Iraq.

“He said that things are going well in Fallujah,” Mr. Bush said, adding that his Iraq commanders had not asked for more troops. The American military has sent up to 15,000 American and Iraqi troops into the battle, backed by tanks, artillery, and attack aircraft.

Lieutenant General John Sattler, the commanding general of the 1st Marine Expeditionary Force, said terrorists had been reduced to “small pockets, blind, moving throughout the city. And we will continue to hunt them down and destroy them.”

“When they attempted to flee from one zone to another, they were killed,” General Sattler said. “We feel very comfortable that none of them moved back toward the north or escaped on the flanks.”

At least 71 terrorists had been killed as of early yesterday, the third day of intense urban combat, the military said. As of Tuesday night, 10 American troops and two members of the Iraqi security forces had been killed. Marine reports yesterday said 25 American troops and 16 Iraqi soldiers were wounded. There was no new report yesterday on American military deaths.

Fallujah, 40 miles west of Baghdad, is the centerpiece of the Sunni Muslim insurgency that has stymied American efforts to secure Iraq and prepare for national elections that are scheduled for January.

The latest kidnappings were part of a surge of attacks outside the city – an attempt by terrorists to divert American-Iraqi forces.

The violence killed at least 28 people across the country yesterday – including 10 who died when a car bomb targeted a police patrol in the capital after sunset. American troops clashed with insurgents in Baghdad and the cities of Ramadi, Mosul, and Latifiyah.

One Marine officer estimated American and Iraqi forces controlled about 70% of the city, but the commander of the Iraqi force said he believed the figure was closer to 50%.

American troops were also skirmishing with insurgents late yesterday in the Wihdah and Muhandiseen neighborhoods, according to Iraqi journalist Abdul Qader Saadi, who said he saw some damaged and burnt armored vehicles and tanks.

Mr. Saadi and other witnesses reported bodies on the streets, with dogs hovering around them. Residents said they were running out of food in a city that had its electricity cut two days ago.

Some wounded Iraqis bled to death, and a family was buried under the ruins of their house after it was bombed by an American jet, Saadi said.

Most of Fallujah’s 200,000 to 300,000 residents are believed to have fled the city before the American assault. Civilian casualties in the attack are not known, though American commanders say they believe the numbers are low.

Fighters charged from the southern parts of the city to back up other insurgents heading to the Jumhuriya district, where there were fierce clashes, he said. Wihdah, Jumhuriya, and Muhandiseen are on the north side of the road that bisects the city.

The American military and the interim Iraqi government are eager to put an Iraqi face on the Fallujah offensive.

Iraqi forces joined American troops in seizing Fallujah’s city hall compound before dawn after a gunbattle with terrorists who hit American tanks with anti-armor rockets. Iraqi soldiers swept into a police station in the compound and raised an Iraqi flag above it.

The Iraqi commander, Major General Abdul Qader Mohammed Jassem Mohan, announced the seizure of the abandoned houses in northern Fallujah that he said contained hostages’ documents, CDs showing captives being killed, and black clothing worn by terrorists in videos.

It appeared troops did not find any of the at least nine foreigners still in kidnappers’ hands – including two Americans. “We have found hostage slaughterhouses in Fallujah that were used by these people,” he said.

But in a reminder of the relative inexperience of the Iraqi contingent, Al Jazeera TV broadcast a videotape yesterday with a terrorist group claiming to have captured 20 Iraqi soldiers. Men wearing Iraqi uniforms were shown with their backs to the camera.

Gunmen also kidnapped three of Mr. Allawi’s relatives from their Baghdad home – his cousin, Ghazi Allawi, the cousin’s wife, and their daughter-in-law, Mr. Allawi’s spokesman said. A terrorist group calling itself Ansar al-Jihad threatened to behead them in 48 hours unless the Fallujah siege is lifted. The claim’s authenticity could not be verified.

The American advance in Fallujah was more rapid than an offensive in April, when terrorists fought a force of fewer than 2,000 Marines to a standstill in a three-week siege. It ended with the Americans handing over the city to a local force, which lost control to Islamic terrorists.

Mr. Mohan, a Sunni who served under Saddam Hussein and later became close to Mr. Allawi, believed the job of running the city should have been given to regulars in the new national army.