Iraqi television has reported that Iraqi troops clashed with US-led forces in the desert near the holy city of Najaf, 160 km (100 miles) south of the capital Baghdad.
The report said the leader of President Saddam Hussein's Baath party in Najaf was killed in the clashes, the closest ground fighting to the capital since US and British forces launched a war against the Iraqi regime on Thursday.
A spokesman for US forces in Kuwait had no comment on the report.
Najaf has a population of around 420,000, and is home to the shrine of Imam Ali, a figure revered by Shi'ite Muslims.