But claims by US spokesmen that their forces were in the centre of the city could not be confirmed by BBC correspondents.
The BBC's Rageh Omaar says he saw no American troops, but saw the evidence of recent fighting littering the main roads, with Iraqi tanks and armoured personnel carriers still on fire.
A spokesman at US Central Command described the operation as the beginning of "rolling patrols".
We have substantial forces now moving into the city
US spokesman Frank Thorp
Iraqi Information Minister Mohammed Saeed al-Sahaf denied the reports, saying Iraqi forces had expelled US troops from the city's international airport and inflicted heavy losses on the Americans.
US Central Command spokesman Frank Thorp said there had been reports of "limited engagements" with the elite Iraq Special Republican Guard.
US military officials are quoted as saying a number of their soldiers have been injured in fighting there.
PUSH FOR BAGHDAD
Map: Details of advances
Baghdad: Iraq's nerve-centre
Opposing forces
The BBC's Andrew Gilligan in Baghdad says the US has a history of premature claims in this conflict and that it is clearly in the American interest to create psychological momentum in the hope that the defenders will give up.
Truckloads of Iraqi troops, some towing howitzers, and heavy Iraqi artillery can be seen moving on the streets of Baghdad for the first time, he says.
I dont doubt that the big one is about to happen soon tho.
[This message was edited by eek on 04-05-03 at 06:59 AM.]