U.S. Army troops seized the southern edge of this key Euphrates River city today as Iraqi militia fighters appeared to retreat in the face of overwhelming firepower.

Hundreds of curious civilians, many of them smiling and waving, lined the narrow, dusty streets while soldiers from the 101st Airborne Division pressed to within a half-mile of the gilded dome of the tomb of Ali, a site venerated by Shiite Muslims as the burial site of the prophet Muhammad's son-in-law.

Shortly before 2 p.m., Maj. Gen. David H. Petraeus, commander of the 101st Airborne, drove in an armed convoy up a rocky escarpment into Najaf, urged on by clapping Iraqis who gestured impatiently for the Americans to press deeper into the city center. An Army loudspeaker truck broadcast messages in Arabic, urging residents not to interfere with the military operation and blaming militia fighters loyal to President Saddam Hussein for the intense fighting of the past week.

American flags flapped from the antennas on two Special Forces pickup trucks, as infantrymen shambled north block by block, cautiously securing intersections and peering through doorways. Young Iraqi men in traditional long robes, called kaftans, stood smoking or chatting, while boys wheeled about on bicycles or two-wheel carts drawn by donkeys.

Four women in black peered over the wall of a second-story terrace. A bearded man clutching his prayer beads peevishly scattered a group of youths who had pressed too close to an Army Humvee armed with a .50-caliber machine gun.

By the end of the day, Petraeus declared Najaf "very much contained." He noted that his troops -- who continue to be wary of snipers and suicide bombers -- have yet to occupy most neighborhoods in this city of about 500,000people 90 miles south of Baghdad, but added, "We seem to have broken the back of the resistance" in the city.

An officer with V Corps, which is directing the Army's drive toward Baghdad, said that when Najaf is taken, "that's huge, that's one big domino. . . . The enemy fought real hard to retain it, and they lost."

Najaf is considered militarily important because it straddles the Army's supply routes leading north to Karbala and the southern approaches to Baghdad. Military planners have been baffled by the indifferent reception given the U.S. invasion by Iraq's often-oppressed Shiite majority, and today's welcome, if hardly tumultuous, was considered heartening.

After intense artillery, tank and air bombardments of suspected Fedayeen strongholds Sunday, the assault on the city reached a climax early this morning when Air Force planes dropped three 2,000-pound bombs on three buildings -- two just north of Ali's tomb and the other just south -- believed to be resistance strongholds. "It looked like sunrise coming up," an Air Force liaison officer said.

As the smoke cleared, hundreds of Iraqi civilians emerged from homes in the old city, waving white cloths and gesturing toward U.S. troops below the escarpment, according to a Special Forces officer. At dawn, seven M1 Abrams tanks, under the cover of AH-64 Apache attack helicopters, drove about a mile into the city from Checkpoint Charlie, a U.S.-controlled intersection on the southern perimeter. Intended as a demonstration of power, the "thunder run" also was intended to topple or crush a statue of Hussein believed to be at an intersection in the center of the city. But last-minute intelligence indicated that the statue was at another intersection, and the tanks pulled back without making contact.

Infantry battalions from the 101st Division's 1st Brigade then pressed into Najaf, first from the southwest, then from the southeast. Several thousand troops from the 2nd Brigade also pressed toward the city from the north. Army officers said they believed the cordon was tight enough to prevent fighters from entering the city, but probably not tight enough to keep some from slipping away.

The number of Iraqi militiamen and their whereabouts tonight remained a subject of more speculation than certainty. While some Special Forces troops had put the number of Saddam's Fedayeen and Al Quds militia fighters at up to 2,000, the number remaining in Najaf this morning was believed to be much smaller, perhaps a few hundred.

Informants indicated that survivors from the dawn bombing had fled north through an enormous L-shaped cemetery abutting Ali's tomb, or through an amusement park. Further operations to secure the city and hunt down resisters were planned for Tuesday.

No casualties from the 101st Airborne were reported. Iraqi civilian casualties in Najaf remain uncertain, although Col. Ben Hodges, commander of the 1st Brigade, said, "It would be almost unfathomable that nobody was injured" during the two-day bombardment.

"We've hit them very hard the last two days, wherever they're firing at us, from homes, from schools. But the one place I've absolutely told them they cannot fire is into the mosque" at the Ali tomb, Hodges said. "I believe they were shocked that we would shoot that close and hit that hard. But look, the gold dome is still standing."

Intelligence operatives said the Shiite clerics here are "still sitting on the fence," and Army officers passed messages asking for help in bringing humanitarian aid into the city. One officer acknowledged that politically, Najaf remains "a confusing situation."

This afternoon an Apache gunship fired on a taxi approaching a checkpoint north of the city; the driver was seriously wounded in the head and was airlifted to a U.S. Army hospital. No weapons or explosives were found in the vehicle, and Petraeus said tonight that he had ordered "a formal investigation to find out what happened."

U.S. troops continued to find large caches of armaments in Najaf, including 2,000 mortar rounds, 20,000 rounds of machine gun ammunition, 1,500 AK-47 assault rifles, chemical protective suits and 25 mortars, which were discovered in a school, Army officers reported. "There is so much ammunition and so many weapons in there, it's unbelievable," Hodges said.

As the 1st Brigade's 2nd Battalion entered the city this morning, an elderly man emerged from a house and pointed out a minefield that contained 69 antitank and anti-personnel mines, Army officers said. A large bulldozer detonated three of the mines with its blade before Army engineers moved forward to clear the field.

Behind the leading companies, Army reinforcements trudged up the steep slope into the city, pulling Javelin antitank missiles and mortar rounds on two-wheeled carts normally used by hunters to haul game out of the woods.

Army officers were heartened by a renewed sense of military momentum and by the near-capitulation of a city that some feared would resist for weeks. But no one was claiming that the outcome in Najaf was likely to be repeated as U.S. forces push up the Euphrates toward Baghdad.

"Every city," one senior officer said, "is going to be different."

A 101st Airborne Division helicopter crew chief, Staff Sgt. Shane Hendrix of Birmingham, Ala., mans a .50-caliber machine gun over a village near Najaf.Army Pfc. Dustin Jans of Phoenix, with the 101st Airborne Division's 1st Brigade, questions Iraqi women at a checkpoint near Najaf. U.S. troops seized the southern edge of the city after two days of intense U.S. attacks.