The AFP newsagency is reporting that a battalion of US army paratroopers have moved into the northern oil city of Kirkuk.
The earlier capture of the city by Kurdish rebels drew warnings from Turkey that a Kurdish occupation was unacceptable.
Ankara has said it has assurances from the Pentagon that American armed forces will take control of the city.
Turkey fears that the formation of any independent Kurdish state could spark separatism among Turkey's own Kurdish population.
The city was pounded by US B-52 bombers early in the morning, helping to trigger an Iraqi collapse.
Residents coming out of the town said Iraqi soldiers there had either laid down their arms or withdrawn south towards Tikrit.
Fierce fighting in Baghdad
It is reported that at least one US soldier has been killed and a number injured in a suicide bomb attack on a military checkpoint in Baghdad.
A US military source said the attack had taken place in Saddam City, an impoverished suburb in the north of Baghdad which is home to two million people, mostly Shiite Muslims.
Meanwhile, US forces say they have established a cordon around Baghdad to stop Iraqi irregular forces entering the city and block any escape by Saddam Hussein loyalists.
Earlier, troops came under heavy fire from fighters loyal to Saddam Hussein.
Iraqi loyalist fighters hiding in buildings, under cars, and beneath bridges attacked US Marines along the northern banks of the Tigris
Fierce fighting took place at a mosque near the river Tigris, where US Marines thought Saddam Hussein might be hiding.
The mosque was defended by members of the elite Special Republican Guard. One Marine was killed and 13 were injured in exchanges of fire.
There were reports of five Iraqi dead and six injured.
In another part of the city, more than 20 dead Iraqis were reported.
Reports of assassination
It is reported that a senior Iraqi Shi'ite leader, Abdul Majid al-Khoei, has been assassinated at the mosque in the holy city of Najaf.
The Reuter newsagency reported he was attacked by a mob and stabbed to death.
It is understood the killing will raise tensions among Iraq's majority Shi'ite population.
Majid was a close aide of Iraq's leading Shi'ite cleric, Grand Ayatollah Ali al-Sistani, who called on the population last week not to hinder the US and British invasion.
Majid was also the son of the late Grand Ayatollah al-Khoei, spiritual leader of Iraq's Shi'ites at the time of the 1991 Gulf War.
Ambassador concedes defeat
Iraq's UN ambassador, Mohammed Aldouri, late last night made the only official Iraqi comments on the day's events, effectively conceding the military loss and the collapse of the government.
'The game is over,' he said in an admission that President Saddam Hussein no longer controlled Baghdad. 'My hope now is peace, for everybody. I hope that peace will prevail and the Iraqi people at the end of the day will have a peaceful life.'
Asked about the whereabouts of the President, the ambassador said he had had no communications with Baghdad for some days.
Rumors were rife overnight that Mr Aldouri was planning to leave on a flight to Paris.
Fears of lawlessness and looting in Baghdad
It is also reported that wide spread looting has taken place agross Baghdad.
Reports say that at least five ministries have been set on fire in the center of the city.
Earlier, Iraqis looted the luxury homes of senior figures of Saddam Hussein's regime, including his son Uday.
The villas of Deputy Prime Minister Tareq Aziz, Saddam's daughter Halah, his half-brother Watban, and army generals, were systematically ransacked in the Jadria and High Babel areas of Baghdad.
The German embassy and the French cultural centre were also sacked by looters today.