Last week CENCO, which deployed more than 40,000 observers to monitor the elections, said it knew who had won the vote but did not reveal who it was, instead urging CENI to publish the results "in keeping with truth and justice".
More than one million people were kept from voting on election day on December 30 because of an Ebola outbreak and militia violence in opposition strongholds mainly in the east of the country.
The church did not name a victor, but reports say it's count finds opposition candidate and businessman Martin Fayulu coming out on top.
Publicly, the church said its tally did not match official results. Two diplomats also said that all major observation missions, including from the African Union and the Southern African Development Community, showed similar results with Fayulu the victor.
"We must have clarity on these results, which are the opposite of what we expected, " Le Drian told CNews.
Nshole urged DRC's population to peacefully await a 14-day constitutional court validation phase, saying those wanting to challenge the result should use legal means.
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The announcement of a victory by opposition presidential candidate Martin Fayulu (who the Catholic Church has indicated was the winner) is unlikely, but would pose high risks of looting by military elements and a coup attempt in Kinshasa. "Mr. Tshisekedi was named by Mr. Kabila and we can not accept a plot against the will of the people".
Congo and the world now face the uncomfortable choice of accepting what could be the country's first peaceful, democratic transfer of power or raising a protest that could lead to violence.
Congo's ruling party responded angrily, calling the church's announcement "anarchist", and the electoral commission accused the church of "preparing an uprising".
Fayulu said the naming of Tshisekedi was the next in a line of stolen elections. He was a vocal activist during the two-year delay in Congo's election, insisting it was time for Kabila to go. He has suggested that the front may have thrown its weight behind Tshisekedi and pushed him to victory.
He is barred from serving three consecutive terms, but during more than two years of election delays many Congolese feared he'd find a way to stay in office.
Tshisekedi's supporters wasted no time in celebrating.
Congo's government cut internet service the day after the vote to prevent speculation on social media.
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Resident John Kabamba says it "may be a message that the publication (of the results) won't meet the expectations of the Congolese people".
Residents of the capital, Kinshasa, said the heavy security presence was a bad sign, with some recalling the violence that followed past disputed elections.
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"This is the coronation of a lifetime", the deputy secretary-general of Tshisekedi's party, Rubens Mikindo, said above the cheers at party headquarters. "This is the beginning of national reconciliation".
By breaking away from the opposition coalition supporting Fayulu, Tshisekedi "positioned himself to bargain with the regime", Englebert wrote.
"The electoral victory of opposition leader Felix Tshisekedi is highly surprising, but the decision makes sense in the context of DRC's political dynamics", said Robert Besseling of EXX Intelligence, a risk consultancy on Africa.
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