People in the Democratic Republic of Congo are anxiously awaiting the outcome of the recent election, with provisional results originally expected on 6 January.
The vote took place more than two years behind schedule, while a court ruled that Kabila could stay in office until the vote was held.
The church's letter to the electoral commission's president comes a day before the expected announcement of the first, partial results of the December 30 election.
"We want the electoral commission to be able to work in good conditions because we want peace and we want the true results to be published", said Fiskas Kalombo, a witness for Fayulu's opposition coalition.
Internal U.N. reports, seen by Reuters, noted allegations of irregularities across the country. "We are progressing well but we do not have everything done yet", said Corneille Nangaa on Saturday without specifying the exact date scheduled for publication.
On the eve of the first expected results of Congo's long-delayed presidential election, President Donald Trump said military personnel had deployed to Central Africa to protect US assets from possible "violent demonstrations", while the country's powerful Catholic church warned of a popular "uprising" if untrue results are announced.
Definitive results are due to be published on January 15, and the swearing-in of the new president three days later, according to this schedule.
In response to protests following the elections, the Congolese government shut down internet services on Sunday.More news: Kanye West's Coachella 2019 Performance 'Collapsed Over Stage Demand'
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More than one million Congolese in opposition strongholds were barred from voting after the electoral commission cancelled the polls there, citing an Ebola outbreak, the second-deadliest in history, and ethnic violence.
The electoral commission's president said it had collected results from about 20 per cent of polling stations, while some Congolese expressed doubt that the first results would be released on Sunday as expected.
The United States urged Congo to release accurate results and restore internet access, warning that those who undermine the democratic process could face US sanctions.
U.S President Donald Trump has said he ordered the deployment of U.S military to Gabon amid fears of violent unrest in neighbouring Democratic Republic of Congo (DRC) after both opposition and ruling party candidates claimed victory in presidential election that ended on Sunday.
The Catholic Church on Thursday said it had information from polling stations that showed one candidate had come out as the victor of the presidential race.
Independent Central Africa analyst Kris Berwouts, meanwhile, said Kabila's administration was "cornered" in the wake of the election. The opposition has been split between two main candidates, Martin Fayulu, a former Exxon Mobil manager who was a relative unknown months ago, and Felix Tshisekedi, the son of late opposition icon Etienne Thisekedi.
Donatien Nshole, the CENCO secretary-general, in a press conference also called on the national electoral commission to publish accurate results. Electoral authorities have indicated a delay might be needed.