Between 2,000 and 3,000 Iraqi fighters were killed as the 3rd Infantry Division moved through southwestern Baghdad, U.S. Central Command spokesman Jim Wilkinson said.

The raid Saturday was the first incursion into the Iraqi capital, and was designed to send a message to both the Iraqi leadership and civilians that coalition forces could move into the city at will, said Air Force Maj. Gen. Gene Renuart. It took troops on a 25-mile run through a corner of Baghdad.

"I know the number that Gen. Franks was briefed on and it was between 2,000 and 3,000," Wilkinson said.

Central Command officials declined to say how they came up with those figures. Previously, they have refused to give Iraqi death tolls.

Wilkinson said while some Iraqi civilians welcomed the troops, other Iraqis put up a fight, including a mixture of Republican Guard and irregular forces.

"I don't want to overstate the heavy fighting. A lot of the time there was no fighting. In some portion of the time, there was fighting," he said.

U.S. officials have said there were limited casualties on the American side.

The blitz took two task forces of the 3rd Infantry Division up from the southern outskirts of the city, past Baghdad University and near the banks of the Tigris River, then back out to the western outskirts of the city to the airport, which is under coalition control.

After the raid, Iraqi Republican Guard, Fedayeen militiamen and other troops were out in force in Baghdad for the first time.