Iraqi soldiers have met fierce resistance in Basra
The radical Shia Iraqi cleric Moqtada Sadr has defied a call by the Iraqi government for his powerful Mehdi Army militia to lay down its weapons.
Arms would only be handed over to an Iraqi government willing to end the US occupation, a senior Sadr aide said.
Skirmishes continued in the city of Basra as Shia militiamen battled security forces, who were backed by at least two US air strikes.
Across Iraq, fighting has claimed an estimated 200 lives since Tuesday.
Government forces have been trying to wrest control of Basra and other Shia areas from the Mehdi Army.
Prime Minister Nouri Maliki on Friday gave the Mehdi Army, which controls large parts of Basra, until 8 April to lay down their arms in return for cash.
He made the offer as an original three-day deadline for them to hand over guns expired.
Haider al-Jabari, a senior Sadr official in the city of Najaf, confirmed there were orders not to surrender arms.
"Sadr has told us not to surrender our arms except to a state that can throw out the [US] occupation," he told AFP news agency.
A UK military spokesman said there were still a number of militia strongholds in Basra, which was "relatively quiet" although there had been "skirmishes".
The Iraqi army was moving into areas of the city in tanks and armoured vehicles and fighting fierce gun-battles, reports from the southern city said earlier.
US jets bombed two sites in the north of the city during the day, the UK military said, targeting what it said were militant strongholds.
Iraqi police said an earlier US air strike on a house in the city killed eight people, although the US has not confirmed the strike.
British forces also fired on what they said was a mortar crew in the north of the city, the first time they have directly engaged the militias since fighting broke out this week.
Coalition forces entered the fray from the air on Friday, with US planes bombing Baghdad's Shia-dominated Sadr City area.
Fighting in Basra has spread to more districts of the city
Fighting also broke out in the city of Karbala on Saturday, with Iraqi security forces saying they had killed 12 "criminals".
Fresh mortar or rocket attacks targeted Baghdad's fortified Green Zone, although there were no reports of casualties.
Estimates vary of the number of deaths since the fighting broke out. Health officials in Baghdad say at least 75 people have been killed in the city in five days.
In Basra, the British military say 50 people have been killed, although local medical sources report as many as 290 dead.
The fighting, which has spread from Basra to Baghdad and other towns such as Hilla and Nasiriya, is blamed on a power struggle between rival Shia factions.
Moqtada Sadr's followers have in the past rebelled against the US-backed government, although the cleric's political bloc has backed Mr Maliki's ruling coalition.
A ceasefire by the Mehdi Army, in place since August 2007 and renewed in February, has been widely credited with reducing sectarian tensions and contributing to the recent overall drop in violence.
Correspondents say Moqtada Sadr's supporters fear the prime minister - also a Shia - wishes to weaken their movement before local elections due later this year.
Mr Maliki vowed that government troops will not leave Basra until "security is restored".
"We will continue to stand up to these gangs in every inch of Iraq," he said on government television. "This is a decisive and final battle."
Meanwhile Al-Jazeera TV broadcast excerpts from an exclusive interview with Moqtada Sadr that it conducted hours before the beginning of the clashes on Tuesday.
Mr Sadr called on Arab and Muslims states and the UN to "recognise the legitimacy of resistance" and offer support to Iraqi to "drive the occupation forces out of its land".