US forces in Iraq say they have killed 64 Shia Muslim militiamen and destroyed an anti-aircraft weapon in fighting near the holy city of Najaf.
US troops are taking over in the Najaf area as the Spanish pull out
The clashes took place on Monday night, hours after US troops had moved into a base in Najaf being vacated by Spanish troops withdrawing from Iraq.
Spain's new leader now says all Spanish forces will be out of Iraq by 27 May.
Meanwhile, there was renewed fighting in Falluja after nightfall, with US artillery reportedly firing on targets.
Sustained blasts were heard for more than 10 minutes in the latest battle, the Associated Press said.
Elsewhere, the Red Cross visited Saddam Hussein for a second time since he was jailed in December.
US military spokesman Brig Gen Mark Kimmitt said the coalition would continue to meet its "obligations under international law" regarding the former leader.
And reports from Baghdad say a US soldier has been killed by gunfire while patrolling a bus station on the eastern outskirts of the Iraqi capital.
Amid the continuing unrest, the US has warned that the new government due to take power in Iraq on 1 July will have to delegate some of its powers to the coalition.
Secretary of State Colin Powell said it was important that coalition troops continued to operate under US command.
The current president of Iraq's US-appointed Governing Council, Massoud Barzani, has said the US has only itself to blame for the military deadlock at Najaf and Falluja.
A supporter of the original US-led invasion of Iraq last year, Mr Barzani said the way the post-Saddam Hussein era had been handled had seen US troops move from being an "army of liberation" to an "army of occupation".
The clashes between US soldiers and Shia militiamen loyal to anti-US cleric Moqtada Sadr - known as the Mehdi Army - took place on the outskirts of the town of Kufa, some 10km (six miles) north-east of Najaf.
Gen Kimmitt said 64 insurgents had been killed, 57 of them in a night-time air strike after US forces spotted an anti-aircraft gun.
Local residents said US warplanes had attacked a Mehdi Army checkpoint near Najaf after fighting between US troops and militiamen broke out in the area.
Buildings used by the militiamen near the checkpoint were badly damaged and at least three vehicles were destroyed, they said.
Sadr has supporters among Iraq's radical Shias
A Najaf hospital official put the preliminary casualty toll from the overnight clashes at 28 Iraqis dead and 32 others wounded.
Mr Sadr is wanted by US forces on charges of ordering the killing of a rival cleric and is currently based in Najaf.
One of his spokesmen described the clash as a provocation, but said the militia remained organised and co-ordinated.
Paul Bremer, the chief US administrator in Iraq, has ordered Mr Sadr to withdraw his militia and its weapons from mosques and schools in Najaf.
For his part, Mr Sadr has threatened to unleash suicide bombers against American forces if they enter the holy city.
The area had been patrolled by Spanish-led forces, but Tuesday saw them evacuate the Najaf area under Spain's pull-out from Iraq.
Plans to begin joint patrols of US marines and Iraqi security forces in the predominantly Sunni Muslim city of Falluja were shelved after heavy fighting there on Monday.
US forces say they are still choosing and training the Iraqi police and civil defence forces that will work alongside them.
The patrols - an attempt to reassert control over the city - are now expected to start later this week.
US forces have taken heavy losses in Iraq this month
Falluja, part of the so-called "Sunni Triangle" in central Iraq, has been a hotbed of anti-US insurgency in the country.
US forces have moved away from threats to carry out an all-out attack on the city unless insurgents hand over their heavy weapons.
"We will take the time necessary to see if there is not a
political solution," Secretary of State Powell