The United States was deeply concerned by the DRC's National Independent Electoral Commission (CENI) decision to deny accreditation to several worldwide election observers and media representatives, it said.
Overall, however, the irregularities did not considerably impact the voting, said Father Donatien Nshole, secretary-general of the church organization known as CENCO.
The church, which deployed some 40,000 electoral observers in all polling centers, can not say publicly who the clear victor appears to be, as Congo's regulations forbid anyone but the electoral commission to announce results. This could be its first peaceful, democratic transfer of power since independence from Belgium in 1960.
"Those who undermine the democratic process, threaten the peace, security or stability of the DRC, or benefit from corruption may find themselves not welcome in the United States and cut off from the USA financial system".
The US State Department spokesman, Robert Palladino, said in a statement: "There are moments in every nation's history when individuals and political leaders step forward and do the right thing".
The U.N. Security Council met behind closed doors to discuss Congo on Friday, at France's request.
According to CENI's timetable, provisional results are due to be published by January 6 - a goal that the commission had reaffirmed just on Tuesday.
Kabila's two-term mandate officially expired in 2016.
But he invoked a caretaker clause in the constitution to stay on, sparking protests that were ruthlessly crushed, leaving scores dead.
Kabila, who is backing Emmanuel Ramazani Shadary to succeed him, claims the elections were fair.
Martin Fayulu who leads the Lamuka coalition and Felix Tshisekedi of the CACH coalition were present at the meeting held at the Hotel Kempinski.
But, he stressed, "these were not able to significantly affect the choice which the Congolese people clearly expressed through the ballot box". Bloodshed followed both the 2006 and 2011 elections.
"We are working around the clock. But if we can't, we can't", Nangaa said. As of Thursday, the electoral commission's president said it had collected results from about 20 percent of polling stations. Results from all 73,000 voting stations would then be consolidated, he said.
"The holding of these elections constitutes, in itself, a first great victory for the Congolese people", it said.