Muhammad Bashar al-Faiyadi, a spokesperson of the Association of Muslim Scholars (AMS), told Aljazeera television minor skirmishes occurred on Sunday, but there were no major clashes.
Al-Faiyadi said the ceasefire would be extended overnight.
The deputy to a member of the US-appointed Iraqi Governing Council Hashim al-Hasani confirmed that talks to try to end fighting would continue on Monday and an informal ceasefire would be extended overnight.
"We reached an agreement to stop the bloodshed until
tomorrow morning in order for us to come back to Falluja to try and stop the bloodshed permanently and completely," al Hasani said.
The head of Falluja's hospital said more than 600 people were killed in the town during this week's fighting.
Two US marines were wounded by sniper fire and an Iraqi was killed, said US marine sources, who accused fighters of not honouring the truce.
The US military said they killed an Iraqi armed with a rocket-propelled grenade, but there was no independent confirmation of this.
Falluja residents are leaving the
city despite the ceasefire
The casualties were reported two hours after the ceasefire.
Abu Muaz, the leader of al-Mujahidiin group spearheading the resistance in the Golan neighbourhood, said they would honour the truce to prevent further bloodshed.
"However, if the enemy breaks the agreement, we will violently respond," he told Aljazeera television on Sunday.
Abd Al-Sattar Abd Al-Jabbar, a member of the AMS, confirmed on Sunday that the two sides had vowed to abide by the ceasefire.
The conditions set for the truce by the resistance included US forces lifting the siege, withdrawal of all forces from the town and compensation for Iraqi casualties in the US air strikes.
Abd Al-Jabbar said US troops would be replaced by Iraqi defence forces.
US officials demanded that those who killed and mutilated four US contractors in Falluja should be handed over together with non-Iraqi fighters. However, the occupation agreed to end the siege without these conditions.
Abd Al-Jabbar in an interview with Aljazeera television denied reports that members of the US-appointed Iraqi Governing Council (IGC) had mediated the truce.
Many residents of Falluja have
found their homes destroyed
Members of the Muslim establishment, including clerics, the AMS and members of the Iraqi Islamic Party, along with Council member Ghazi al-Yawar had brokered the ceasefire, he said.
Al-Yawar had threatened to pullout of the IGC over the siege in Falluja.
Abd Al-Jabbar criticised the IGC for not doing enough during the siege of Falluja, which left more than 1000 people injured. He said among the dead were 157 women.
The 12-hour ceasefire began on Sunday at 0600 GMT. A senior member of the Iraqi Islamic Party, Hatim al-Husayni, said the truce would pave the way for a gradual withdrawal of US marines from Falluja.
Meanwhile, residents of Falluja continued to flee their homes on Sunday, reported Aljazeera. Many are seeking refuge in Abu Ghraib, about 20km from Baghdad, where residents held up banners welcoming them.
Women and children were seen sitting crammed in the back of pick-up trucks with hastily packed personal belongings.
Many Falluja residents were angry with the IGC and the Arab League for not doing enough to lift the siege off the city.
Elsewhere, a US Apache attack helicopter was shot down west of Baghdad on Sunday, killing its two crew members, said the US military.
A US army Apache helicopter flies
Heavy fighting took place in the area for a third straight day.
Large palls of black smoke were seen rising from the nearby area of Abu Ghraib, where at least four helicopters were seen hovering.
Another US soldier died of wounds received in fighting last week in the town of Baquba, north of Baghdad, the US military said.
Also in Baquba, one civilian was killed and six were wounded when US soldiers and Iraqi paramilitary opened fire by mistake on a minibus.
Lieutenant Muhammad Abd Al-Karim said the police had been given information that a minibus was believed to be carrying resistance fighters in Baquba.
An occupation spokesman said he had no information about the shooting.
Seven loud explosions were also heard in the Green Zone where US forces are based in Baghdad and columns of smoke were also seen rising from the area, Aljazeera's correspondent said. Occupation sources said they had no details on the explosions.
In the southern city of Basra, British occupation headquarters came under mortar attack late on Saturday, reported Aljazeera's correspondent. There were no reports of casualties.