Najaf, Iraq ? A Shiite insurgency appeared to be weakening Tuesday night as Iraqi forces moved to within 200 yards of the revered Imam Ali Shrine and Iraq’s defense minister once again demanded fighters loyal to a radical cleric surrender or face a violent raid.

The militant force, which once waged fierce battles with U.S. troops throughout the Old City and Najaf’s vast cemetery, seemed considerably diminished in number and less aggressive after days of U.S. airstrikes and relentless artillery pounding.

Early today, U.S. forces launched heavy bombing strikes on the volatile city of Fallujah, residents said.

U.S. warplanes strafed targets on the city’s eastern outskirts, and explosions could be heard for over two hours.

Both the Iraqi government and the U.S. military say no military moves are being made without the approval of interim Prime Minister Ayad Allawi.

Hundreds of insurgents have been spotted leaving Najaf in recent days, witnesses said. Those that remained appeared to have pulled back to the area around the shrine, where the fighting Tuesday was concentrated, U.S. troops said.

Police say radical Shiite cleric Muqtada al-Sadr, who has not been seen in public for days, had fled the city.

His aides, however, vigorously denied that, saying al-Sadr was in a secret hideout here. Regardless, the fiery, charismatic cleric’s absence from the battlefield may have withered his followers’ morale.

U.S. warplanes bombed the Old City late Tuesday for the third night in a row, witnesses reported. Huge blasts rumbled throughout the city for about 10 minutes followed by gunbattles and smaller explosions.

Earlier in the day, fierce fighting broke out near the shrine compound, with rockets launched from U.S. helicopters kicking up clouds of smoke and debris. Bradley fighting vehicles patrolling the nearly deserted, bullet-scarred streets attacked militants, who responded with mortar fire and rocket-propelled grenades.

“We are under constant enemy small-arms, mortar, and RPG attack,” said U.S. Lt. Chris Kent, whose unit was about 300 yards from the compound. “U.S. forces are consolidating positions to allow for future operations. Morale is very high.”

Masked Shiite militiamen armed with rocket launchers and automatic weapons pour through the streets and set up roadblocks to protest U.S. military action in Najaf, in the southern Iraqi city of Basra. About 200 militiamen supporting firebrand Shiite cleric Muqtada al-Sadr blocked roads Tuesday in Basra with burning tires and broken concrete blocks.

Iraqi forces, accompanying U.S. troops into the Old City for the first time in recent days, combed through the neighborhood, approaching as close as 200 yards to the shrine, controlled by militants loyal to al-Sadr.

Both the Iraqi government and the U.S. military say no military moves are being made without the approval of interim Prime Minister Ayad Allawi.

Defense Minister Hazem Shaalan, addressing Iraqi National Guard troops in Najaf, said Tuesday that Iraqi forces would head toward the shrine “tonight” to await the signal for a raid or the capitulation of the militants.

“When your brothers approach the holy shrine compound, they will direct calls of mercy to those (militants) to surrender,” Shaalan told the troops. “They have hours to surrender.”

By late Tuesday, there was no indication Iraqi forces had advanced on the shrine.

Shaalan made a similar threat a week ago, saying the government could raid the shrine by the end of the day last Wednesday to free it of “its vile occupation.” The government later backed down and said it would work for a peaceful solution.

Any raid on the shrine, the holiest Shiite site in the country, risked igniting a massive Shiite rebellion throughout Iraq against the fledgling interim government, already battling a persistent and bloody Sunni insurgency.