The Independent National Election Commission (CENI) began to give the results from legislative and provincial elections that took place in parallel, a process expected to take several hours, and this would be followed by the outcome of the presidential vote.
As the lengthy results were read out on nationwide TV, police were deployed at strategic spots in the capital Kinshasa where, for the second evening running, many residents went home and locked their doors early.
Kabila, 47, was due to step down two years ago but clung to office, sparking widespread protests that were repressed at the cost of scores of lives.
The elections were held on December 30, but CENI last weekend said provisional results, expected on Sunday, would be held up because of logistical problems.
The long delay sparked blunt warnings from inside and outside the DRC, but also coincided with an apparent overture to Kabila from opposition leaders.
According to the initial timetable, after provisional results are released, definitive results are due on January 15 with the swearing-in of the new president three days later.
After deploying tens of thousands of its own election observers, the powerful Catholic Church last week said it knew the outcome of the ballot and called on the authorities to reveal the result "in keeping with truth and justice".
Campaign groups on Wednesday called for the immediate release of the results and told people "to be prepared to go out onto the streets in massive numbers" if the outcome failed to accurately reflect the vote.
"Results contrary to the truth of the ballot box will be considered as a constitutional coup," said a joint statement from the groups, which include Lucha (Struggle for Change) and Filimbi.
South Africa and Zambia, DRC's neighbour to the south, joined the clamour to publish the results.
"The delay in releasing the results of the elections can lead to suspicions and compromise peace and stability of the country," South African President Cyril Ramaphosa and Zambian counterpart Edgar Lungu said in a joint statement.
The turmoil surrounding the election revived traumatic memories of the DRC's brutal past.
The mineral-rich country has never had a peaceful transition of power since it gained independence from Belgium in 1960.
Bloody clashes marred elections in 2006 and 2011, and two wars between 1996 and 2003, drawing in armies from around the region, claimed millions of lives.
When Kabila announced last year he would step down after 18 years in power, he hand-picked a loyalist, former interior minister Emmanuel Ramazani Shadary, as his party's candidate.
The choice fuelled accusations that Kabila -- concerned about possible retribution -- would use Shadary to protect his interests after the vote.
But on Tuesday, the opposition hinted at a rapprochement.
"There's no spirit of revenge," said Felix Tshisekedi, the candidate of the longtime opposition UDPS party.
He also told the Belgian newspaper Le Soir that Kabila could be honoured for ushering in a peaceful transition.
"Mr Kabila is a Congolese citizen. He has a place here in Congo. He will do what he wants. The constitution is clear -- he (as former president) will be a senator for life. The keyword for us is: There's no revenge." Fayulu is backed by former Katanga governor Moise Katumbi, considered a traitor by Kabila, and ex-warlord and former vice president Jean-Pierre Bemba.
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