The last-minute extension by African Union mediators came after an initial deadline to reach a deal expired at midnight, throwing into doubt two years of talks to end fighting which left tens of thousands dead.
The decision to extend the deadline followed a request from the US, which said the extra time would allow for agreement on two critical security issues.
The parties will be given more time to discuss the disarmament of the government-backed Janjawid militia, who are accused of rape, murder and looting, and the integration of rebel forces into the army.
"We are not going to accept this document for signature unless there are fundamental changes made to the document," Ahmad Tugud, the Justice and Equality Movement (JEM) chief negotiator, said.
The UN describes the conflict as
the biggest humanitarian crisis
The government of Sudan said earlier it was ready to sign the plan drafted by the AU mediators, but one of the factions of the Sudan Liberation Army (SLA) said it would not sign the proposed agreement unless its demands were met in full.
"If the proposal does not include all our demands we will not sign," Saif Harun, spokesman for the SLA faction led by Minni Arcua Minnawi, told reporters.
It was not immediately known what the position of the other SLA faction - a third rebel group involved in the fighting - was on the 85-page draft peace settlement.
Talks have been under way in the Nigerian capital of Abuja between the Sudanese government and rebel representatives, in an attempt to reach a deal in the presence of AU and international mediators.
An earlier meeting ended with Jan Pronk, the UN representative for Sudan, urging them to sign the deal.
Sudan had earlier announced that it had agreed to accept the AU offer.
"The government ... wishes to confirm its decision to formally accept this document and its readiness to sign it," said a statement from Majzoub al-Khalifa, head of the government's negotiating team.
"The government wishes to confirm its full commitment to implement the agreement in good faith. The delegation is also fully convinced that any difficulties that might come up in the implementation stages can be resolved by consensus between all the parties."
"We are not going to accept this document for signature unless there are fundamental changes made to the document"
Justice and Equality Movement (JEM) chief negotiator,
The Chida International Hotel in Abuja was packed with diplomats and Sudanese representatives, as pressure increased to strike a deal.
Several previous deadlines have passed without any apparent impact on the discussions.
Rebels took up arms in early 2003 in ethnically mixed Darfur, an arid region the size of France, over what they saw as neglect by the Arab-dominated central government.
Khartoum used proxy militias drawn from Arab tribes to crush the rebellion. The fighting has killed tens of thousands of people while a campaign of arson, looting and rape has driven more than two million from their homes into refugee camps in Darfur and neighbouring Chad.
All sides have continued fighting despite a 2004 ceasefire, according to the AU which has 7000 peacekeepers in Darfur.
George Bush, the US president, said "genocide in Sudan is unacceptable" and endorsed a series of "Save Darfur" rallies taking place across the United States on Sunday, organised by a coalition of more than 160 religious and humanitarian groups.
Aid groups say increased fighting in Darfur has made it impossible to deliver food and medicine to tens of thousands of refugees in Darfur and in camps across the border in Chad.