Vote counting was transparent, 59 percent of polling places it observed opened on time and police securing the polls behaved professionally, the organization added.
More than a third of polling stations in the December 30 election were missing voting materials when polls opened, according to a CENCO report on Thursday which outlined various shortfalls in the election's organization.
The Congolese election commission said logistical problems may force it to postpone publication of provisional results from Sunday's vote, which also included elections to the national parliament and provincial assemblies.
At stake is the political stewardship of a mineral-rich country that has never known a peaceful transition of power since independence from Belgium in 1960.
Tension has risen further over the marathon counting process with opposition fears running high that the result will be rigged to favour Mr Kabila's preferred successor, Emmanuel Ramazani Shadary. Speaking after the meeting, France's United Nations ambassador only said the Security Council is keeping close watch on vote counting in the presidential election in Congo.
Democratic Republic of Congo's Catholic bishops conference (CENCO) said on Thursday that results from Sunday's presidential election in its possession show that one candidate has clearly won, but did not say which one.
"The African Union and other governments should make clear to Congo's leadership that any manipulation of the election results will have serious consequences", said Ida Sawyer, deputy Africa director at Human Rights Watch.
The U.N. Security Council was briefed behind closed doors on the latest developments on Friday at the request of France.
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The government has also shut down the internet, blocked SMS messages and restricted the media, casting a shadow over the vote's credibility.
Congo's ruling party on Friday called the church's attitude "irresponsible and anarchist". Provisional results are expected on January 6, with the final outcome on January 15. It will hold another meeting on the issue on Tuesday.
The United States demanded that "accurate" election results be released, warning of sanctions against anyone who undermined the fledgling democracy.
Observers reported irregularities amid the balloting.
Kabila's government refused to accredit election monitors from the European Union and the USA -based Carter Center, which said there were widespread irregularities in the 2011 election.
A spokesman for Felix Tshisekedi, one of two opposition candidates, said the hold-up was a further sign of fraud.
The country lived through two fully-fledged wars between 1996 and 2003 that claimed millions of lives through bloodshed, fighting, starvation and disease.