There have been sporadic exchanges of fire in Falluja, as efforts continue to bring an end to a week of fighting between US forces and Sunni insurgents.
The US began its offensive in Falluja on Monday
Mediators from the US-appointed Iraqi Governing Council who visited the city say they secured a 12-hour ceasefire from 0600 GMT on Sunday.
Both sides pledged to respect the truce for a few hours, despite reports of shooting in the besieged city.
The relative pause came as insurgents shot down a US helicopter near Baghdad.
The US military said the crew was killed when the AH-64 Apache gunship came down near Abu Ghraib - a town that has seen heavy fighting in recent days.
"We have a quick reaction force on site conducting a recovery of the equipment and the personnel and our hearts go out to the families," said Brig Gen Mark Kimmitt.
In Falluja two marines were wounded by snipers and an Iraqi man was killed in one of several clashes since the ceasefire began, a US military spokesman said.
Marines have allowed some to leave Falluja - after a thorough search
Despite the sporadic exchanges both sides say they intend to maintain the truce for at least the next few hours.
US civil administrator in Iraq, Paul Bremer, said the ceasefire came at the request of members of the Iraqi Governing Council.
"I understand that the ceasefire for now is holding and we're hopeful that we will be able to get some productive talks going," he said in a taped interview.
The BBC's Richard Lister in Baghdad says what happens after that is unclear.
Iraqi politicians suggest that the American troops will gradually withdraw from the city, to be replaced by Iraqi forces.
The US military leadership in Baghdad has insisted that those responsible for the killing and mutilation of four American security guards in Falluja must be handed over for prosecution.
Thousands of Falluja residents took advantage of Sunday's lull to leave the city.
Some gave accounts of the recent fighting.
"As soon as the Americans see a group of people in the streets, they shoot at them," one man told AFP.
"I saw people bury their dead in their yards because they feared to venture out," he added.
Hundreds of Falluja residents are said to have died in the past week.
A reporter for the London-based Daily Telegraph
in the city has said he saw the bodies of two Germans, following reports that two German embassy security guards had gone missing.
They were killed while travelling from Jordan to Baghdad on Wednesday, the report said.
The German foreign ministry later said the two were probably dead.
Iraqi negotiator Qahtan al-Rubaie said a ceasefire call had been issued by tribal, religious and community leaders in Falluja.
Noriaki Imai, 18, Japanese researcher
Nahoko Takato, 34, Japanese aid worker
Soichiro Koriyama, 32, Japanese photojournalist
Nabil George Razuq, 30, Palestinian aid worker
Fadi Ihsan Fadel, 33, Canadian aid worker
Thomas Hamill, 43, US civilian worker
He was speaking after the delegation returned to Baghdad and met US officials, including Paul Bremer.
He told Reuters news agency it was hoped that the ceasefire would open the way for talks on a possible withdrawal from Falluja by US marines.
Iraq's new national security adviser, Muwaffaq al-Rubaie, told the BBC that much of the violence is localised and a reaction to 35 years of repression under Saddam Hussein.
He said he was confident Iraq would be able overcome its difficulties and become a model of democracy for the region.
"Iraq will be the Japan for the Middle East," he told BBC's Talking Point.
Meanwhile the deadline given by kidnappers of US civilian Thomas Hamill, who threatened to kill him unless US troops ended the Falluja operation, passed with no indication about his fate.
There is still no news on the three kidnapped Japanese civilians. Their abductors were reported to have said they would release their hostages on Sunday.
A British civilian Gary Teeley, who was kidnapped in the southern city of Nasiriya six days ago, has been handed over to coalition forces there and is safe and well, the Foreign Office in London said.