The US-appointed Iraqi Governing Council has called for an immediate ceasefire, as US forces battle Sunni militants for a sixth day in Falluja.
Reports from Falluja say food and medical supplies are low
The council said a political solution needed to be found to the crisis in the besieged city, west of Baghdad.
One member called the Falluja operation "genocide" after doctors there reported 450 deaths and 1,000 injured this week.
A US general urged the militants to join in a bilateral ceasefire, after a attempted truce failed on Saturday.
"This is an aspiration," General Mark Kimmit told reporters in Baghdad.
He said he was "hoping to get this message to the enemy through this
Earlier the Governing Council said the fighting should stop now.
"We call for an immediate ceasefire and for ... political solutions for situations in some parts of the country," it said in a statement.
The BBC's Caroline Hawley in Baghdad says the council is furious that it was not consulted about the Falluja offensive.
A spokesman for the council told the BBC the crisis could have been avoided.
One Sunni Muslim member, Ghazi Ajil al-Yawer, said he was ready to resign over the Falluja crisis.
"How can a superpower like the US put itself in a state of war with a small city like Falluja? This is genocide," he told AFP news agency on Friday, the first anniversary of the fall of Saddam Hussein.
The Iraqi interim Human Rights Minister, Abdel Basit Turki, and a member of the Iraqi Governing Council's rotating presidency, Iyad Allawi, both resigned on Friday.
In Washington, US Secretary of State Colin Powell said the Shia and Sunni rebellions had proved stronger than expected.
IRAQ ONE YEAR ON
US military deaths since 'major combat over' on May 1 2003: At least 514
Other coalition deaths: At least 67
Total reported Iraqi civilian deaths: Estimates from 8,865 to 10,715 *
$33bn allocated so far for reconstruction
More than 200,000 recruited to Iraqi security forces
Oil exports up to 1.8m barrels a day, against 2m pre-war
Electricity back to pre-war levels
51 million new "Baath-free" textbooks in schools
170 newspapers in print
46 of 55 'most wanted' captured or killed, including Saddam
* Iraqi Body Count, to 8/04/2004
** Coalition Provisional Authority
But he insisted that plans to hand over sovereignty in June were going ahead.
On Saturday civilians were reportedly trying to leave Falluja, as fighting continued.
On Friday US troops suspended their offensive, allowing women and children to leave.
Men were stopped as the Americans searched for suspects in the killing and mutilation of four US security guards in Falluja at the end of March.
Fighting later resumed. Gunfire and mortar blasts echoed across the city late on Friday.
Local commanders said they tried to keep the truce but had responded when fired at by militants.
Meanwhile Moqtada Sadr, the radical cleric whose followers have been directing violent unrest in Shia areas since Sunday, has demanded the withdrawal of coalition troops from Iraq.
Speaking in a sermon read out at Friday Prayers in the town of Kufa, he said the US could no longer point to Saddam Hussein or weapons of mass destruction as reasons to be in Iraq.
"You are now fighting an entire nation, from south to north, from east to west, and we advise you to withdraw from Iraq," said Mr Sadr, who is the subject of a coalition arrest warrant.
The US has reported the deaths of at least 42 of its soldiers in combat since Sunday.
Militants are holding a number of foreign nationals hostage, including three Japanese citizens, two Palestinians and a Canadian.