The lull in fighting comes after US helicopters and planes bombed the Golan area Tuesday night, injuring at least one person and destroying a house and some cars, Aljazeera's correspondent reported.
"No exchange of fire has erupted and nothing has been heard except for the sounds of US helicopters looming over the area," Abd al-Adhim Muhammad said, reporting from Falluja on Wednesday.
But despite the relative peace, the city was almost paralysed, he added.
Also, informed sources told Aljazeera a meeting between US troops and the delegation representing Falluja residents would take place on Wednesday.
The sky lit up Tuesday night as strike after strike targeted the Golan district of the city. Aljazeera's correspondent reported a heavy exchange of gunfire and several homes on fire.
He added that US marines were not only attacking from the air with helicopter gunships and warplanes, but ground troops were using machine guns and tanks as well.
Bremer postponed joint patrols
because of Saddam's birthday
The fighting came hours after a US deadline for fighters in the city of 300,000 to hand over their weapons. More than 600 people have been killed since US marines besieged the city on 5 April.
Also, US-led occupation said they planned to stage joint patrols of the city with local police.
The patrols initially were scheduled to start on Tuesday, but US overseer in Iraq Paul Bremer told Iraqi television they would start on Thursday.
Marine officers said the decision took into account sensitivity for the birthday of ousted president Saddam Hussein, which falls on Wednesday.
Falluja has become a touchstone for the aggrieved and long dominant Sunni minority in Iraq and has attracted wider attention in the mostly Sunni Arab world.
The US-led occupation authority blames the fighting there on "anti-Iraqi forces" they say comprise foreign fighters with possible al-Qaida connections and former members of Saddam Hussein's ousted government who are disgruntled at losing their privileges.
Washington would like to have restored a more stable situation before handing back technical sovereignty to Iraqis on 30 June.
However, US officials have made clear their military will retain wide powers after that date.