A spokesman for the Sudan Liberation Movement (SLM), Ibrahim Bahar, told journalists in the Nigerian capital that his group was suspending talks until the situation improves.
He accused Khartoum of ignoring a truce deal signed during a previous round of negotiations.
Another rebel spokesman, Muhammad Ahmad Tugod – chief negotiator of the Justice and Equality Movement (JEM), said the situation in Darfur was deteriorating and applauded SLM’s decision to pull out of talks.
African Union comment
But the Abuja conference’s African Union mediators expressed the hope that the groups could be persuaded to change their minds and said they would attempt to reconvene the talks on Tuesday at 10am (0900 GMT).
“We have no alternative but to come to this conclusion … in order to stop all the military activities going on in Darfur,” he added.
The African Union’s lead mediator, Sam Ibok, said all the international representatives at the talks had advised against the walk-out because there was no justification for such a suspension.
Sudan government position
Meanwhile, Sudanese government spokesman Ibrahim Muhammad said: “Only negotiation and talks will solve the problem of Darfur. Withdrawal from the talks means more trouble for Darfur.”
SLM rebels have been fighting for
The Darfur region has been ravaged by civil conflict since February last year, when two armed opposition groups launched a rebellion against the government, demanding autonomy and a greater share of the nation’s wealth.
Rebel leaders claim that Khartoum has marginalised and persecuted Darfur‘s mainly black African settled inhabitants, and responded to the uprising by arming nomadic Arab pro-government militias.
More that 70,000 people have been killed and 1.6 million driven from their homes since the start of the fighting, according to the United Nations.
Charity workers killed
Several hours before the talks broke up, two Sudanese men working for British charity Save the Children were killed when their convoy came under fire in South Darfur state, the United Nations said.
The killings have seen UN humanitarian operations in the state suspended.
Medical assistant Abu Bakr al-Tayyib and mechanic Yaqub Abd al-Nabi Ahmad died on Sunday when their convoy of clearly marked humanitarian vehicles came under fire, a UN spokeswoman said in a statement.
Save the Children operates a feeding centre and medical clinics in the area, added Radhia Achoure.
“Our humanitarian operations in South Darfur are currently suspended whilst we review the situation. An African Union investigation is under way,” the statement added.
Sunday’s killings were the second fatal incident suffered by Save the Children staff in two months.