US President George W Bush has called the Iraqi government offensive against militiamen in Basra "a defining moment in the history of a free Iraq".
Iraqi Prime Minister Nouri Maliki has set a deadline for the Mehdi Army, which still controls large parts of the city, to lay down their arms for money.
Correspondents say the militia has so far ignored the ultimatum.
More than 130 people have been killed and 350 injured since a clampdown on militias began in Basra on Tuesday.
Mr Bush said the actions of Mr Maliki, a Shia, showed he treated Shias and Sunnis equally if they broke the law.
He told a White House news conference: "Any government that presumes to represent the majority of people must confront criminal elements or people who think they can live outside the law - and that's what's taking place in Basra."
Moqtada Sadr's supporters at Friday prayers in Sadr City Battles threaten fragile Iraq
On Wednesday, Mr Maliki gave the militiamen 72 hours to hand over their arms, threatening "severe penalties".
On Friday, he extended the deadline by 10 days and offered cash for their guns.
A statement from his office said: "All those who have heavy and intermediate weapons are to deliver them to security sites and they will be rewarded financially. This will start from 28 March to 8 April."
Defence Minister Abdel Qader Jassim said the government had been "surprised" by the fighters' resistance and had "been obliged to change our plans and our tactics".
Blinking first?
The BBC's Paul Wood in Baghdad says the deadline extension means Mr Maliki - who has taken personal charge of the Basra offensive - has blinked first.
Some 30,000 troops and police are fighting the Mehdi Army, which is loyal to radical Shia cleric Moqtada Sadr and had been formally on ceasefire for the last seven months.
But after four days of battle, the militia remains in control of some large, densely-populated areas.
BASRA KEY FACTS
Mr Sadr's supporters - known as Sadrists - were part of a Shia political bloc that helped thrust Mr Maliki to power in 2005, but our correspondent says the prime minister now views the group as a threat.
He says the military action of the past few days is partly designed to pre-empt Sadrist gains in elections in southern Iraq scheduled for October.
Mr Maliki has no militia of his own, our correspondent says, but has allied himself with groups such as the Badr Corps, which are heavily represented in the security forces that he, as prime minister, commands.
US-led forces joined the battle for the first time in the early hours of Friday, with air strikes in Basra and Baghdad.
A US military spokesman in Baghdad, Maj Mark Cheadle, told AP news agency: "As you know, we've been getting attacked and going after the enemy all day."
Iraq's parliament called an emergency meeting to discuss the crisis, which has also brought a three-day curfew to Baghdad.
But just 54 MPs out of 275 managed to get inside the fortified Green Zone to attend the session, because it was under fresh bombardment from mortars and rockets.
One of the missiles hit Iraqi Vice-President Tareq Hashemi's offices, killing at least one guard.
The fighting between security forces and militiamen has spilled over in recent days to other Iraqi towns and cities, including Karbala, Hilla, Kut, Diwaniya and Nasiriya.
Aid agencies in Geneva say the upsurge in violence has made Iraq's already poor humanitarian situation "critical".
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