Fresh fighting has erupted in the Iraqi city of Najaf, as Prime Minister Iyad Allawi made a "final call" for cleric Moqtada Sadr to end his insurgency.
US troops are deployed around the shrine
At least seven policemen were killed and more than 20 wounded in a mortar attack against a police station.
And smoke could be seen in the area of the Imam Ali shrine where Mr Sadr and his supporters are based.
Mr Allawi declined to say whether there was a deadline for Mr Sadr to dismantle his militias and leave the holy sites.
"I can't put a date yet," the prime minister told journalists at a news conference in Baghdad, flanked by senior government ministers.
The minister of defence said his forces were ready - but they were giving negotiations another chance.
The cleric has said he will end the uprising only if there is a truce. And some of his aides rejected the latest ultimatum.
But he is coming under pressure both militarily and psychologically, says the BBC's Matthew Price in Baghdad.
US troops there say they have made a major advance since Wednesday, when they went on the offensive in Sadr City - the mainly Shia area of Baghdad that is a stronghold of Mr Sadr.
Heavy explosions were reported in the area around the Imam Ali shrine in Najaf on Thursday.
Television channels showed pictures of plumes of smoke rising from the scene.
A cabinet minister had earlier described Mr Sadr as an "outlaw" and said his Mehdi Army militiamen had "only hours" to leave the Imam Ali shrine, or face military action.
"We have been preparing for a military offensive for five days to put an end to this crisis," Kasim Daoud told a news conference in Najaf.
The government's demands, according to Mr Daoud, are:
- Mr Sadr must hold a news conference to promise not to resort to future violence and announce the disarming of his Mehdi Army militia
- His fighters must hand in their weapons
- They must vacate Najaf's holy sites
But Mr Sadr's aides said he rejected the ultimatum and did not recognise the authority of Mr Daoud.
However, he remained committed to ending the stand-off through negotiations, they said.
On Wednesday, Mr Sadr addressed a message to the Iraqi national conference, offering to withdraw from the shrine if the American and Iraqi forces besieging him agreed to a truce first.
Residents of Baghdad's Sadr City told the BBC there was fierce fighting overnight between the Americans and Shia militia.
Our correspondent, reporting from the outskirts, says the Americans appear to have moved into the heart of the district in great numbers.
He saw two disabled US tanks which he said had probably been hit by rocket-propelled grenades, and he could also see more tanks deployed along one of the main roads.
Fighters loyal to Moqtada Sadr remain defiant
The situation was calm, he reported, although residents contacted by the BBC said they were stuck in their houses, unsure whether it was safe to come out.
An American soldier was killed in the fighting, a military statement reported by French news agency AFP said.
Another US soldier was wounded during the assault on the suburb, which is home to about two million people.