Fayulu, told RFI that the results were an "electoral coup", adding that the provisional results "have nothing to do with the truth at the ballot box". Last week, the Catholic Church said their observations showed a clear victor, and many say that was Fayulu.
Kabila says he wants to stay in politics and may run again in 2023, when he will no longer be barred by term limits.
The African Union said it "took note" of the result and warned any dispute over the outcome should be "resolved peacefully".
Belgium said it would use its temporary seat on the U.N. Security Council to also seek clarification.
French Foreign Minister Jean-Yves Le Drian said the surprise result was the "opposite to what we expected", based on field observations of the December 30 vote that was marred by voting machine malfunctions and Ebola virus outbreaks.
The vast, mineral-rich Central African country is choosing a successor to departing President Joseph Kabila, in power since 2001. Congo's constitutional court has 14 days to validate them.
"Kabila will be able to influence Tshisekedi, who now owes his ascendancy to power to Kabila's control of the electoral commission", Mr. Besseling told AFP.
However, runner-up Martin Fayulu, who is also an opposition candidate, has described it as an "electoral coup".
The electoral commission (CENI) announced on Tuesday evening that it had initiated "a series of evaluation meetings and deliberations, at the end of which it will proceed to the publication of provisional results from the presidential election".
Two civilians and two policemen were killed Thursday and another 10 people injured when a protest erupted in the western city of Kikwit, a Fayulu stronghold, police said.
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The announcement of DRC's 30 December election results will likely be delayed to March or April (while four excluded localities vote), effectively extending the administration of incumbent President Joseph Kabila through this period.
But election chief Corneille Nangaa declared Tshisekedi the victor with 38.57 percent of the vote, just ahead of Fayulu with 34.8 percent.
The global community has not congratulated Tshisekedi on his victory. He is barred from serving three consecutive terms, but until he announced past year that he would step aside many Congolese feared he'd find a way to stay in office.
There were celebrations in parts of Kinshasa and the south of the country, where Tshisekedi has broad support.
"This is the coronation of a lifetime", the deputy secretary-general of Tshisekedi's party, Rubens Mikindo, said shortly after the announcement that his candidate had won, above the cheers at party headquarters.
Some said they would be happy as long as Fayulu or Tshisekedi won, while recalling the violence that followed past disputed elections. "This is the beginning of national reconciliation".
Asked whether the president-elect is a professional qualified to be President, Mr. Apea argued: " Looking at the past leaders that Africa has had, together with the many broken promises they have uttered, Felix Tshisekedi, is overqualified".
But in the run-up to the results, Tshisekedi said Kabila had nothing to fear should he come to power, comments analysts interpreted as efforts to reassure the president and his supporters that interests accumulated over two decades in power were not at risk.