Aljazeera TV quotes a resistance leader as saying Falluja's fighters will respect a 12-hour ceasefire.
The two sides have agreed that the ceasefire will come into effect from 0600GMT on Sunday to pave the way for US marines to leave the town.
The US-led occupation army had offered to observe a temporary truce from midday on Saturday to allow mediators and al-Sadr supporters to discuss a possible end to the clashes.
Earlier, Alaa Makki, a senior member of the Iraqi Islamic Party which was leading mediation efforts for the truce told AFP the fighters in Falluja have given the delegation "a series of conditions for the ceasefire, including a pullout of US forces from Falluja into the surrounding desert."
"They did not give a specific area for the pullout, but logically it would be around five kilometers," he said.
"They also asked for opening the entrances to the city to allow people as well as food and medical supply to enter easily and for people to bury their dead," he said.
The US-led occupation authorities has "asked for a ceasefire, for handing over those who took part in the mutilation and repeated riots."
"The demands of the two parties are logical and should be easy to satisfy," he said.
"We are all very hopeful because we have been given promises from the two sides, the only difficulty would be in the mechanism of the implementation of the ceasefire because it concerns military operations on the ground," he said.
Al-Sadr in talks
Meanwhile, several members of the US-appointed Iraqi Governing Council are negotiating with Shia leader Muqtada al-Sadr to end a Shia uprising in the centre and the south of the country, a member of the council said on Saturday.
Nasir al-Chaderji declined to give details of the talks, but said a deal would have to include al-Sadr's renunciation of violence and a commitment by the authorities to improve the lot of his mostly impoverished supporters.
"They are in direct contact with Muqtada. We are already seeing calm in Sadr City and we are encouraged by the situation in Najaf as we go into a major religious celebration," Chaderji told Reuters.