Iraq's government has extended by 10 days a deadline for Shia militiamen fighting troops in the southern city of Basra to hand over their weapons.
More than 130 people have been killed and 350 injured since a clampdown on militias began in Basra on Tuesday.
US-led forces joined the battle for the first time overnight, bombing Shia positions, the UK military said.
Aid agencies say the upsurge in violence has made Iraq's already poor humanitarian situation "critical".
Speaking in Geneva, the International Committee of the Red Cross, Unicef and the International Organisation for Migration (IOM) called on all the warring parties to allow the passage of food and medical supplies.
Unicef said it was gravely concerned about the health consequences for children, warning that some families had barely two days of drinking water supplies left.
Moqtada Sadr's supporters at Friday prayers in Sadr City Battles threaten fragile Iraq
The IOM said the fighting could add to the 2m Iraqis already internally displaced.
Meanwhile, a statement from Prime Minister Nouri Maliki's 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."
BBC Arab affairs analyst Magdi Abdelhadi says the extension indicates either the military solution is proving more difficult than Mr Maliki thought or there are behind-the-scenes negotiations for a peaceful resolution.
Defence Minister Abdel Qader Jassim said the security forces had been caught off-guard by the scale of the militiamen's fight-back.
"We were surprised by this resistance and have been obliged to change our plans and our tactics," he was quoted as saying by Reuters news agency.
'Defining moment'
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.
President George W Bush called the battle "a defining moment in the history of a free Iraq".
BASRA KEY FACTS
"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," he told a White House news conference.
Iraq's parliament called an emergency meeting to discuss the crisis, which has 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.
UK military spokesman in Basra Maj Tom Holloway said US warplanes had for the first time in the operation carried out bombing raids overnight in the city, targeting "mortar teams" and "a concentration of militia troops".
The Iraqi prime minister has vowed to continue the fight against the militias for as long as necessary.
Mr Maliki has personally overseen the operation in Basra, which involves some 30,000 troops and police fighting the Mehdi Army, led by radical Shia cleric Moqtada Sadr.
With the militia remaining in control of some densely populated areas, the prime minister has pulled out of this weekend's Arab League summit in Syria to deal with the crisis.
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