"As of noon today coalition forces have initiated a unilateral suspension of offensive operations in Falluja," Paul Bremer said on Friday.
But the US-led occupation's deputy director of operations, Brigadier-General Mark Kimmitt, denied the reports of a ceasefire.
Minutes after Bremer's announcement, US forces carried out a fresh offensive on Falluja, bombing the town from the air. Scores of residents were injured in the attack, reported Aljazeera's correspondent.
"There is no brokered agreement for a ceasefire in Falluja," Kimmitt said. "There is no agreement between the rebels and the coalition forces."
Earlier, the Iraqi Governing Council member Mohsin Abd al-Hameed in a statement on behalf of his Iraqi Islamic party to Aljazeera, said military action in Falluja would end for a period of 24 hours.
Upon commitment to a ceasefire by the occupation forces and Iraqi resistance fighters the ceasefire would continue, the statement said.
The Islamic party political bureau would send a delegation to hold talks with prominent figures in the town, the statement said.
Aljazeera, meanwhile, has learned that during negotiations to end the military offensive, US forces imposed many conditions including getting the Aljazeera crew out of the town.
At dawn on Friday, US forces asked the residents to evacuate the town, reported Aljazeera's correspondent.
Innocents have lost lives in
This was preceded by US bombardment since late on Thursday. Helicopters were seen hovering after the bombings.
Violent clashes also erupted between US forces and resistance fighters.
US tanks too reached central Falluja and bombed the Golan area as well as Nazzal, Zubat and Askari.
The bombardment destroyed 10 houses while three went up in flames. Aljazeera's correspondent witnessed a large family arriving at the hospital with two of its members dead.
Other members were still under debris, he said, adding that one shrapnel hit a pregnant woman while another pierced the eye of a child.
Ambulances were bringing in casualties all night while people have started fleeing the city fearing more attacks.
Men, women and children were fleeing on foot through backstreets and paths that cut through fields, carrying small bags, food and medicines.
Most were seen heading towards the nearby village of Naimiyah, south of Falluja, which has been under effective US siege since Monday.
Bodies were left to rot in the streets as people cowered indoors.
On Thursday, the US marines tried to enter the neighbourhoods of Zubat and Nazzal but the Shia militia pounded them with anti-tank rockets and mortar fire, forcing them to retreat.
The fierce confrontations have left more than 300 people dead and over 500 wounded, hospital sources said.