Kabila's second and final five-year term ended on December 20, but he has shown no intention of leaving office soon, sparking violent protests that have left at least 40 people dead this week, according to the United Nations.
The influential Catholic Church has been brokering talks between the government and opposition and hopes rose this week of an imminent deal, with a draft seen by AFP outlining plans for fresh elections at the end of next year, when Kabila would step down.
"The work is practically finished - the final touches are all that is left to do before the deal is signed," insisted Marcel Utembi, president of the Congo National Episcopal Conference (CENCO), who had pushed for a deal before Christmas.
But others indicated there was still a long way to go.
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"Everything is still blocked on how (public affairs) will be managed during the transition period," said opposition delegate Francois Muamba.
A frustrated CENCO official, speaking on condition of anonymity, blasted DR Congo's political class for "serious mediocrity" in their inability to reach a deal.
"They have called into question everything we arranged the day before," the official said as talks stretched into the night.
Time is pressing as the bishops overseeing the talks are due to quit the capital this afternoon to return to their congregations in time for Christmas Eve mass.
Congolese police put the toll at 20 dead, saying they had largely been killed in "looting" or by "stray bullets".
Other sources say somewhere between 56 and 125 people have been killed in a week of clashes, not counting the unknown toll from fighting between security forces and an anti- government militia in the central town of Kananga.
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