Only last week the sides appeared near a historic deal that could have paved the way for the first peaceful transfer of power through a democratic election since the country gained independence in 1960.
However, the talks hit a stumbling block over whether a new prime minister for Democratic Republic of the Congo will come from the main opposition bloc and on the composition of the electoral commission, which the opposition accuses of pro-government bias.
“At this stage, we are closer to a rupture than to a solution,” opposition leader Félix Tshisekedi said in a tweet.
However, one negotiator held out hope that agreement could be reached.
“We believe that we can find an accord today,” said Archbishop Fridolin Ambongo, one of the Roman Catholic bishops mediating the talks. “If we are here it is because we believe that.”
Despite running past 3pm (1400 GMT) when a signing ceremony in the capital Kinshasa had been planned, Ambongo said negotiators had reached compromises on several outstanding points.
If the negotiations fall apart, the church plans to call off the talks and move ahead with a “Plan B” which the bishops have yet to make public.
Appointment of a prime minister is the one remaining sticking point, said Martin Fayulu, an opposition delegate.
A spokesman for the ruling coalition declined to comment.
Other parties and mediators made no comment.
The talks between the ruling coalition and opposition parties organised by the Catholic Church were set to resume for a make-or-break day at the headquarters of the conference of Catholic bishops in the capital Kinshasa.
Delegates said bishops acting as mediators met Kabila and veteran opposition leader Etienne Tshisekedi on Thursday.
Under the deal, Kabila would agree not to attempt to change the constitution to participate in elections to be held next year.
His two-term mandate ended on December 19 but the authorities have effectively extended it until 2018.
That would have represented a significant turnaround given that security forces killed around 40 people last week for protesting the tenure of a leader who came to power in 2001 when his father Laurent was assassinated.
The opposition also wants the authorities to drop charges against some of its leaders, arguing that the prosecutions are political.
On Wednesday a political opposition leader was sentenced to five years in prison.
The court found Franck Diongo, president of the opposition MLP party, guilty of illegally detaining three soldiers during violent protests last week in the capital Kinshasa that killed dozens, said Georges Kapiamba, a lawyer and human rights advocate who attended the trial.
Kapiamba told Reuters that Diongo was not able to defend himself because of failing health and called the decision “totally political”.
The government has denied that the prosecution is politically motivated.
A political deal could boost pro-democracy activists in other countries, given the Congo’s size and sway on the continent.
But if the talks break down it could lead to more violent demonstrations.
Police spokesman Colonel Pierre Mwanamputu said security was being stepped up for the New Year celebrations and to guard against unrest.
The Congo has never seen a democratic transfer of power following polls since independence from Belgium in 1960.
Two decades ago, the country collapsed into the deadliest conflict in modern African history.
Its two wars in the late 1990s and early 2000s pulled in at least six African armies and left more than 3mn dead.