U.S. ground forces moving toward Baghdad are fighting Saddam Hussein's elite Republican Guard troops near the Shiite Muslim holy city of Karbala in central Iraq. The U.S. Army's 3rd Infantry Division says the Republican Guards have attempted to use women and children as human shields.

The 3rd Infantry Division began a limited offensive Monday morning in an area southwest of Baghdad to secure bridge sites and to identify mortar and artillery positions of Republican Guards believed to be in the area.

As one armored unit of the 3rd Infantry Division moved into the town of Hindiyah on the Euphrates River, U.S. troops began taking fire from a battalion-sized force of Republican Guards armed with rocket-propelled grenades, mortars and artillery.

American soldiers took up positions behind abandoned Iraqi bunkers and traded fire with Iraqi troops for more than 30 minutes. The fighting was the first significant contact American ground forces have had with Republican Guards since the war began 12 days ago.

The battle was not over. U.S. Army Lieutenant-Colonel Gary Luck said a large number of Iraqi troops re-emerged a couple of hours later using women and children as human shields. "One woman attempted to escape. She ran toward the river. She was shot in the back," he said. "We were able to obscure her with smoke, send out a rescue team and got physical control of her and evacuated her and she is being treated right now. Don't know her condition at this time."

The 3rd Infantry Division says its forces have inflicted heavy casualties on Republican Guard troops who have attempted to re-enforce positions across the Euphrates River. They say they also captured several dozen Iraqis. There are no reports of U.S. casualties.

The Republican Guards, the best-trained and equipped military force in Iraq, have formed a ring around Baghdad, guarding the most likely avenues of attack by coalition forces.

In Washington Sunday, the head of the Joint Chiefs of Staff, General Richard Myers, said days of relentless air-strikes have reduced some Republican Guard units to less than half of their pre-war fighting ability.

It is still unclear when coalition forces will fully engage the Republican Guards in battle. U.S. military commanders say they want to be sure the number of Republican Guard troops, tanks and artillery are sufficiently reduced before launching any major assaults to capture Baghdad.