Iraq's Prime Minister Nouri Maliki has given Shia militants in the southern city of Basra 72 hours to lay down their arms or face "severe penalties".
Mr Maliki issued the threat on the second day of a government offensive, that has left at least 46 people dead.
The leader of the main militia, the Mehdi Army, says Mr Maliki must leave Basra and start negotiations.
The clashes have spread elsewhere with rockets fired at Baghdad's Green Zone, causing a number of injuries.
Many Iraqi towns are under curfew.
Unrest in Basra has been stoked by a variety of militias and criminal gangs.
But the government's unspoken intent is to stop it falling under the sway of the Mehdi Army, led by the radical young cleric Moqtada Sadr, BBC Middle East analyst Roger Hardy says.
As night fell, Basra was quieter, after a second day of intensive fighting, concentrated on the districts of Gazaiza, Garma, Khmasamene, Hayania and Maqal.
BASRA KEY FACTS
Third largest city, population 2.6 million approx
Located on the Shatt al-Arab waterway leading to the Gulf - making it a centre for commerce and oil exports
Region around city has substantial oil resources
4,000 UK troops based at international airport
About 225 people are said to have been injured. A Basra city council member said there were few civilian casualties as they were staying inside their houses.
A large number of gunmen have been detained, say officials.
British forces, which patrolled Basra for nearly five years, withdrew to a base outside the city in December and have not been involved in the fighting.
Prime Minister Maliki has been overseeing the operation from Basra.
"We are not going to chase those who hand over their weapons within 72 hours," Mr Maliki said.
"If they do not surrender their arms, the law will follow its course," the Basra Operational Command quoted him as saying.
Hours later, a senior aide to Moqtada Sadr, Hazim al-Araji, told the BBC that the Sadrists would be willing to send a delegation to meet Mr Maliki for talks if he left Basra.
But events might overtake any efforts at dialogue, says the BBC's Crispin Thorold in Baghdad.
Black-shirted members of the Mehdi Army have reappeared on the streets of Sadr City in Baghdad. They had been withdrawn when the movement declared a ceasefire last August.
Across the Iraqi capital, the thud of rockets and mortars has been heard - several fell short of their target, the Green Zone - home to the diplomatic and government offices - killing at least eight civilians.
Inside the heavily-fortified zone three Americans were seriously injured.
In Sadr City, a vast Shia suburb in the capital, there were overnight clashes between Mehdi Army fighters and American and Iraqi soldiers.
Up to 20 people died in the violence and at least 115 people have been injured, according to police.
Here and in other Shia areas of Iraq, many shops and offices are shuttered, indicating Moqtada Sadr's call for a campaign of civil disobedience is being followed.
More clashes also broke out in Kut, south-east of Baghdad, where at least three people were reported dead on Wednesday.
Sadrists are convinced the operation is an attempt to weaken them ahead of provincial elections due in October, but Mr Maliki has embarked on a risky strategy, says the BBC's Roger Hardy.
For one thing, it is far from clear that it will succeed, he says.
The Sadrist movement enjoys widespread support, especially among the young and the poor, and is well entrenched in Basra and many other predominantly Shia towns and cities in the south.
For another, if the ceasefire which the Sadrists have largely followed were to collapse, that would seriously undermine claims by the government - and by the Bush administration in Washington - that Iraq was moving from civil war to political reconciliation, our correspondent says.
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