The US State Department also called on the commission to release accurate results from the election in a statement Thursday.
"The announcement of voting trends by Priest Nshole is likely to brainwash the population while preparing an insurrection that CENCO alone will be responsible for", commission president Corneille Nangaa wrote in a letter to CENCO president Marcel Utembi, seen by Reuters. An exact new date has not been announced.
The country's Catholic church has warned about a popular "uprising" if false election results are announced, according to The Associated Press.
The National Episcopal Conference of Congo (CENCO), which represents the country's Catholic bishops and has been at the forefront of protests calling for Kabila to step down, urged the electoral commission to publish the results "in keeping with truth and justice".
"We have observed that the Congolese people have chosen a candidate as president of the republic", Donatien Nshole, secretary general of Cenco, told RFI's Sonia Rolley in an interview broadcast on Friday.
The government refused to accredit election monitors from the European Union and the US-based Carter Centre, which said there were widespread irregularities in the 2011 election.
The government has already cut internet access across the vast Central African country to prevent any speculation on social media about who might have won the election.
"This being a very sensitive, a very tense period, we are concerned that these efforts to silence dissent could backfire considerably when the results are announced", a spokeswoman for the United Nations human rights office, Ravina Shamdasani, said Friday, also noting intimidation of journalists, observers and rights activists.
Harris half century gives Australia solid start in Sydney
They have kept going at Australia on a very flat pitch, despite the batsmen's efforts to throw them off their lines and lengths. When the series started, it was the Australian batting which was under scrutiny in the absence of David Warner and Steve Smith.
The electoral commission said voting could not take place in the eastern cities of Beni and Butembo because of a deadly Ebola outbreak in the region.
Lamuka coalition leader Felix Fayulu debunked the SADC position saying the poll was deliberately disorganised to favour the ruling party candidate.
Western powers and DRC's neighbours hope sub-Saharan Africa's biggest country will see its first peaceful transition of power since independence in 1960.
The United States is urging Congo's government to release accurate results of its presidential election and warns that those who undermine the democratic process could face US sanctions.
Donald Trump announced Friday the United States was sending about 80 troops to Gabon to deploy in the event of election-related unrest in nearby DR Congo. According to the report, only the electoral commission is allowed to announce the victor.
In a letter to congressional leaders, Trump said the first of about 80 military personnel arrived in Gabon on Wednesday in case they are needed to protect USA citizens and diplomatic facilities in Congo's capital Kinshasa.
Opinion polls that were released three days to the elections by the New York University, an affiliated Congo Research Group, put Mr Fayulu in the lead with 44 per cent, followed by Mr Tshisekedi at 24 per cent and Mr Shadary at 18 per cent.