Opposition candidates are concerned over the use of the electronic voting machines, which they fear will allow massive fraud. Electoral authorities say the machines will make the ballot more efficient.
The final results of the presidential vote will be published on January 15, and the next president will be sworn in on January 18, CENI said, without explaining how this would dovetail with the delayed vote in the troubled regions.
The Democratic Republic of Congo, the second biggest country in Africa, has a long history of political turbulence and violence.
It has never had a peaceful transition of power since it gained independence from Belgium in 1960.
In 1996-1997 and from 1998-2003, it became the theatre of two wars that left millions of dead and homeless and sucked in countries from around central and southern Africa.
Wars are unfolding in the east, where militia groups are carrying out bloody attacks.
The CENI statement pointed in particular to North Kivu, in the grip of “a terrorist threat” and “a dangerous, ongoing epidemic of Ebola virus” in the areas of Beni and Butembo.
At the other end of the country, in Yumbi territory, violence this month had caused an exodus and led to the destruction of election equipment, it said.