After a short morning lull, US marines fired MK-19 grenades as blasts and gunfire continued to be heard in the city.
During the night, heavy mortar fire was heard.
Late on Saturday, mediators said resistance fighters, US-appointed Iraqi Governing Council (IGC) members and US-led occupation authorities had agreed to a 12-hour ceasefire beginning on Sunday at 0600 GMT after six days of fierce clashes which claimed the lives of more than 450 people and injured more than 1000.
"The two sides have agreed to observe a 12-hour ceasefire on Sunday at 10am (0600 GMT)," a senior member of the Iraqi Islamic Party, Hatim al-Husayni, said.
"This will pave the way for the gradual pullout of US marine troops from Falluja," he said after a meeting with US-led occupation officials in Baghdad on his return from the mediation talks.
Also present at the talks were members of the Iraqi Islamic Party (ISP) and the Association of Muslim Scholars (AMS), the highest Sunni authority in Iraq.
Among the conditions set for a truce by resistance fighters were that US-led occupation forces lift the siege imposed on Falluja, withdraw all forces from the town and compensate Iraqi casualties of the US air strikes over the town.
More than 450 have been killed
in Falluja in six days of siege
US occupation officials demanded that those who killed and mutilated four US contractors in Falluja should be handed over together with other non-Iraqi fighters who fought with resistance fighters.
Falluja on Saturday came under intense fire from occupation forces with US warplanes striking the city at least twice in the early hours.
Two people were injured as several bombs were dropped on different parts of the city. And at least one Iraqi - a 75-year old man - was killed by sniper fire, Aljazeera's correspondent said.
Some residents told Aljazeera they were unable to transport the injured to hospitals due to the volatile situation.
CIA officers killed
Aljazeera aired a tape showing the bodies of two men reported to be US intelligence officers killed in Falluja.
A voice on the videotape said the two Americans were CIA officers working in Iraq.
The burnt car belonging to the
two Americans killed in Falluja
The videotape, broadcast on Sunday, showed the bloodied bodies of two foreign men lying on the ground, one shot in the back and another in the leg, surrounded by several Iraqi men. It was not clear when the footage was filmed or by whom.
There are at least two US soldiers, several contractors and two German embassy security guards missing in Iraq.
Meanwhile, several loud explosions have echoed across Baghdad in the early hours of Sunday morning and smoke rose near the headquarters of the US-led occupation in the heavily fortified Green Zone.
The US occupation told Aljazeera it had no immediate information on the cause of the blasts.
Gunfire could be heard in central Baghdad after the blasts.
Four Iraqis were killed in clashes with US occupation forces in the northern Iraqi city of Kirkuk overnight, a police officer said on Sunday.
"[US-led occupation forces] should lift the siege imposed upon Falluja, withdraw all forces from the town and compensate Iraqi casualties of the US air strikes over the town"
Some conditions set by Falluja resistance fighters for truce
"Four people were killed and many suspects were arrested in the clashes between armed men and US soldiers in three Shia districts," Colonel Khattab Abd Allah Arif said.
"The four dead were armed men who attacked US forces," he added, noting that the clashes lasted throughout the night.
Tension was running high in the city on Sunday with a large deployment of US forces while local police kept a low profile.
Elsewhere in Iraq on Saturday, seven Iraqis were killed in the town of Kut, among them five children and a woman, Aljazeera's correspondent reported.
In Baghdad, an Iraqi was killed on Saturday when a US tank opened fire at a group of citizens trying to protect al-Rawda al-Kadhimiya (Imam Kadhim shrine) in Baghdad, according to Aljazeera's correspondent.