Shia Iraqi militants have fought running battles with US-led security forces in the holy city of Najaf and in Basra and the capital, Baghdad.
The Shia militia are said to be a small but well-trained force
A US helicopter was shot down over Najaf, with its crew injured, amid the heaviest fighting in the area since a ceasefire was called there in June.
At least 10 people, including one US soldier, died in the fighting.
But spokesmen for militant cleric Moqtada Sadr said he wanted to renew the truce reached with US forces.
That agreement came after Mr Sadr's Mehdi Army militia, which draws on radical elements in the country's majority Shia Muslim community, began armed resistance to the US-led occupation in April.
Spokesmen for the cleric in both Najaf and Baghdad said on Thursday night that he wanted to continue the ceasefire.
"Sadr announced that we are committed to the truce and that [US] forces must honour the truce," said one, Ahmed al-Shaibany, speaking to the Associated Press news agency in Najaf.
Tension has been building in Najaf in recent days and fighting finally erupted on Thursday morning, the BBC's Alastair Leithead reports from Baghdad.
The governor of Najaf requested back-up from US marines after the main police station was attacked, the US military said, but a spokesman for Mr Sadr said US forces and Iraqi police had attacked first.
Iraqi hospital sources said at least seven Iraqis had been killed and dozens injured.
One US soldier was killed and five others wounded in an ambush on a convoy outside the city, the US military said.
A correspondent for AFP news agency said the streets of Najaf were deserted after the clashes in the city centre and at a cemetery.
In Basra, at least two Mehdi Army members were killed in a 15-minute gunfight with UK troops.
A local Sadr spokesman, Sheikh Saad al-Basri, said the militia would fight a jihad against "foreign troops" and any Iraqi security forces who backed them after four men were arrested by the British.
Gunmen also fought US troops in Baghdad's Sadr City area, wounding seven of them, the US military confirmed. An unconfirmed report said five Iraqi civilians were also killed.
Several mortar bombs exploded late on Thursday near hotels in central Baghdad but no-one was reported hurt.
Earlier, there was a bomb attack on a police station in Mahawil, south of Baghdad.
At least six people were killed and 20 others hurt when an attacker drove a minibus up to the police station and detonated explosives.
Separately, gunmen shot dead two police officers in the Mahawil area.