US President George W Bush has said the coalition in Iraq is "making pretty good progress" in stabilising the holy city of Najaf, despite heavy fighting.
US and Iraqi troops have been fighting Sadr militia for five days
US forces are battling supporters of Shia cleric Moqtada Sadr, who rejected an appeal for his militia to leave.
The two sides continued fighting on Tuesday for a sixth consecutive day.
On Monday Polish-led multinational forces ceded military authority in two Iraqi provinces to US marines because of worsening security.
In Najaf intense fighting was reported on Tuesday around the city's vast cemetery - the scene of fierce clashes on Monday.
There were also explosions in the capital, Baghdad, as insurgents fired mortar rounds and rockets at targets in the city.
In other developments:
- UK troops remain on high alert after Monday's killing of a British soldier in clashes with militiamen loyal to Mr Sadr on the streets of Basra
- a 16-hour curfew was imposed on Baghdad's Sadr City, where US-led forces have clashed regularly with supporters of Mr Sadr.
- threats from Mr Sadr's fighters against oilfields in the south of Iraq forced production to be halted, officials said
- four lorry drivers - two Jordanians and two Lebanese - were reportedly freed by Iraqi militants.
US ordered change
The US military spokesman in Baghdad, Major Jay Antonelli, told the BBC that a 24-hour truce called to allow the wounded to be evacuated from Najaf was "no longer in place", blaming enemy attacks.
The news that the multinational force was giving up control of Najaf and Qadisiya provinces came in a Polish military statement.
The change was ordered by the senior US officer in Iraq, Gen George Casey, the statement said.
It added that the Americans would not be subject to the multinational mandate, which does not allow combat operations.
The multinational force retains control of three other provinces in the area.
Praise for Poland
Shortly after the announcement about control of Najaf, Polish Prime Minister Marek Belka met US President George W Bush for scheduled talks at the White House in Washington.
Mr Bush was asked if, following the fighting against Mr Sadr's forces, the US policy was still to capture or kill him.
"Our policy is to work with [Iraqi] Prime Minister [Iyad] Allawi and support the Iraqis as they move toward elections," he said.
Bush praised his Polish allies
"Our troops were engaged against Sadr's militia and so were the Iraqis, and it appears we're making pretty good progress about stabilising Najaf."
Mr Bush praised the role played by Polish troops in Iraq.
Asked about Polish opinion polls suggesting 73% of Poles want their troops to leave Iraq, Mr Belka said no-one wanted to stay in Iraq forever, although he added that the two men had not talked about specific timings for a withdrawal.
The BBC's Dan Griffiths in Washington says the situation in Iraq is putting a strain on the traditionally strong relationship between the US and Poland.
Our correspondent says US marines have been in nominal control of the Najaf area since Spain withdrew its troops after a change of government in March, and the handover by Polish troops confirms that position.
Rocked by explosions
Mr Sadr has rejected Iraqi government calls for his men to leave Najaf and vowed to defend the city.
"I will stay in holy Najaf and will not leave it," he told a news conference on Monday. "I will stay here in defence of holy Najaf because it is the holiest city and I will stay there until the last drop of my blood."
Artillery and tank fire rocked the city in the latest clashes.
The fighting erupted in Najaf on Thursday, when members of Mr Sadr's militia clashed with Iraqi police and governor Adnan al-Zorfi requested American support.
The violence broke a ceasefire agreed in June.
The number of casualties in Najaf is unclear.