|The toppling of a huge statue was a symbolic moment|
The marines came under attack - probably by special Republican Guard units - as dawn broke along the Tigris river, the BBC's David Willis says.
One marine was killed in a half-hour battle, says our correspondent, who is travelling with the marines.
US tanks have taken up positions in the heart of Baghdad after a day which signalled the end of Saddam Hussein's hold on the city.
The US Secretary of Defence, Donald Rumsfeld, has described the scenes of celebrating Iraqis as "breathtaking and historic".
Many Iraqis barricaded themselves in their blacked-out homes overnight for fear of looting and lawlessness.
A BBC correspondent in Baghdad says distant explosions continue as US troops consolidate their control, but he says the Americans have not yet filled the power vacuum.
Mr Rumsfeld has warned the fighting is not over, and admitted US-led forces did not have full control of the capital.
"The task is to see that the regime is not there. There is a good portion of the country where that has been achieved, but there's a good portion of the country where that has not been achieved," he told reporters in Washington.
Mr Rumsfeld said Saddam Hussein was "taking his place in the pantheon of failed brutal dictators".
There is still no confirmation of whether Saddam Hussein is alive or dead following Monday's bombing of a building in Baghdad where the Iraqi leader was believed to be with his two sons.
Other key developments:
As the Iraqi leader's hold on Baghdad crumbled, US and British warplanes on Wednesday continued to attack Saddam Hussein's hometown Tikrit, about 145 kilometres (90 miles) north of Baghdad.
US Central Command said the air strikes were targeting the Republican Guards' Adnan division, "shaping the battlefield" for US ground troops.
|CENTRAL BAGHDAD |
Map: Fighting in Baghdad Who are the Shia?
But the Americans have admitted they do not yet control several other important towns in central Iraq - including Kut, south-east of Baghdad.
Further south, British forces around Iraq's second city, Basra, said they still need to restore order and eliminate the last remnants of Iraqi resistance.
The commander of British forces in the Gulf, Air Marshall Brian Burridge, said it would be a few more days before the aid agencies could resume their work in the city, which still lacks water and basic medical supplies.
UK troops have offered a gun amnesty in an effort to restore order to Basra.
In northern Iraq, US special operations forces and Kurdish fighters have seized a small town 24 kilometres (15 miles) north of Mosul and captured more than 200 Iraqis, according to coalition Central Command in Qatar.
As US-led troops move to consolidate their positions in Baghdad, a BBC correspondent in the capital says nothing can erase the euphoria on Wednesday, in which television pictures of the toppling of a massive statue of Saddam Hussein were beamed live around the world.
In a symbolic moment, an American armoured vehicle helped a crowd of cheering Iraqis to pull down a huge statue in the Fardus square in front of the hotel.
Dozens of exultant people leapt on the deposed figure and stamped on it, shouting "Death to Saddam!"
The day had begun with cheering Iraqis greeting marines arriving in the Shia stronghold of Saddam City.
Iraqi looters ransacked United Nations offices, and the Olympic Committee building - headquarters of Saddam Hussein's elder son Uday - was set on fire.