A democratic handover would break ground for Congo's 70 million people who since independence from Belgium in 1960.
Congo's volatile political crisis rumbled on Friday after church-led talks were forced into another day, edging closer to the legal limit for President Joseph Kabila to hold on to power.
The country's Catholic episcopal conference, CENCO, had set Friday as the deadline to get the government and opposition to agree on a transition for the country after Kabila's second and last legal term expires on Tuesday.
An election for a new Democratic Republic of Congo head of state was supposed to have been held this year, but the authorities failed to organise the polls.
The 45-year-old president, who stepped into his assassinated father's shoes in 2001 and is now ruling for a second elected term, is barred from a third mandate under the constitution.
Opponents accuse him of delaying the vote in the hope of tweaking the constitution to extend the Kabila family's hold over a nation hugely rich in minerals that is almost the size of western Europe.
The international community has warned the current tension could lead to spiralling violence.
Some two decades ago, Congo sunk into the deadliest conflict in modern African history, its two wars in the late 1990s and early 2000s dragging in at least six African armies and leaving more than three million dead.
The CENCO-sponsored talks launched early this month pit the ruling party and fringe opposition groups against a mainstream opposition coalition headed by veteran Kabila rival, Etienne Tshisekedi, who is 84.
Sources close to the talks had said early on Friday a deal was closing in on the date and organisation of a presidential vote.
But later CENCO mediators returned from meeting members of Kabila's cabinet, declining to speak to the press and resuming talks with the rival groups behind closed doors.
Discussions will resume at 0800 GMT on Saturday, they later said. But that round will be limited as Congo's bishops will leave Saturday for a long-planned visit to see Pope Francis.
The main sticking point in any future deal is the political fate of Kabila, who true to his reputation as a man of few words, has not announced his plans.
A democratic handover would break ground for Congo's 70 million people who since independence from Belgium in 1960 have never witnessed political change at the ballot box.
And in the last few years hundreds of people have died in political violence in the capital, Kinshasa, and elsewhere.
Tshisekedi and his allies had threatened nationwide protests from Monday to press Kabila to step down, but have opted to hold off pending the negotiations.
"If we win guarantees (on an election date and a pledge that Kabila will not seek a new mandate) we will speak to the people because the challenge begins from December 19," Jean-Marc Kabund, the secretary-general of Tshisekedi's party, told AFP.
The government for its part has ordered that social networks including Facebook and WhatsApp be blocked from 11:59 pm (2259 GMT) on Sunday.
Police said they were setting up checkpoints in large Congolese cities to "discourage criminal intentions that have started to take on worrying dimensions".