BAGHDAD, Iraq (CNN) -- In a symbolic strike against Saddam Hussein's crumbling regime, Iraqis and U.S. Marines on Wednesday pulled down a towering statue of the Iraqi leader at Baghdad's center.

Marines watched as dozens of Iraqis tied a rope around the statue in Firdos Square and then took turns pounding at the base of the monument with a sledgehammer. An American M-88 tank recovery vehicle, equipped with a large crane, moved in a few minutes later to help pull the statue crashing to the ground.

The Marines put a chain around the neck of the statue and covered its head with a U.S. flag briefly, before replacing it with an Iraqi flag. That flag also was removed before the statue was pulled down.

Iraqis then jumped and stomped on the statue, which had been erected last April 28 to celebrate Saddam's birthday, and then pulled its head through the streets.

Those Marines were greeted by journalists and cheering Iraqis as they took up positions in central Baghdad, but fierce fighting raged elsewhere in the Iraqi capital.

"We thought we were going to get a lot of resistance but we never did, so we just kept pushing and pushing until we got here," said Cpl. Steven Harris with the Marines in the square.

It was a different story for a U.S. Marine column moving into Baghdad from the east, which came under heavy fire Wednesday afternoon at Baghdad University after being greeted by cheering Iraqis earlier in the day.

CNN Correspondent Martin Savidge, embedded with the 1st Marines, 7th Battalion, said the university campus was a battlefield, with black smoke rising from several buildings and machine-gun fire ripping around the fighting vehicles.

"This was not the exact reception ... anticipated," Savidge reported while under fire. "There's a lot of smoke and dust now and fire. ... [It's] a far cry from the jubilant crowds ... just hard to imagine two blocks away."

Savidge said the fighting ignited an ammunition cache on the campus, which burned and exploded for about 45 minutes after the Marines secured the area.

Fighting also continued in northeast Baghdad, according to Roland Huguenin-Benjamin with the International Committee of the Red Cross. He said a Red Cross convoy was hit, and no one had been able to reach the wounded because of the crossfire.

In the Baghdad suburb of Saddam City, residents were in the streets, celebrating the apparent end of the Iraqi regime. A Shiite Muslim leader told a group of 400 to 500 people, "The tyrant of the world is finished, thanks to the coalition. Thank God for Iraq the victorious."

International media showed video of looting in and around Baghdad. Dozens of people were seen hauling off furniture, fixtures and office supplies, using wheelbarrows and pickups, with no security forces to stop them. Others ripped down posters of Saddam and destroyed them -- kicking, punching and spitting on the pictures.

Residents in the northern Iraqi city of Erbil spilled out onto the streets as well in passionate but less-raucous demonstrations, waving flags, tossing confetti and chanting.

At a briefing Wednesday at U.S. Central Command headquarters in Qatar, Brig. Gen. Vincent Brooks said coalition officials were somewhat concerned about the unrest but said they believe it will "settle down in due time."

"I think in this case we're seeing a lot of jubilation and people who have long been oppressed for years and years having choices," Brooks said.

Saddam's fate remains a mystery after Monday's B-1 bomber strike on a Baghdad building where U.S. officials suspected he was meeting with senior aides, but coalition officials said that there were signs that his regime was losing control of the country, even before Wednesday's demonstrations.

A senior U.S. Army officer said Wednesday that "the majority of Iraqi forces [in the Baghdad area] have now given up."

Iraqi Information Minister Mohammed Saeed al-Sahaf, who been the public face of the Iraqi government during the war, did not appear Wednesday for his daily briefing. The government minders, who have shadowed international reporters for the last 12 years, were not at the Palestine Hotel, which is the base for many journalists, CNN's Rula Amin reported.

The U.S. Army has airlifted more armor into a coalition-controlled air base in northern Iraq early Wednesday, preparing for a push south along the northern front.

Tanks, armored personnel carriers and Bradley fighting vehicles were moved from a base in Germany to Harir airfield, near the city of Erbil, where the Army's 173rd Airborne Brigade is deployed, reported CNN Correspondent Steve Nettleton, embedded in the area.