The country's two major observer groups deplored the shutting down of the internet, and Bishop Abraham Djamba, head of Congo's Symocel observation mission, asked the government to restore it.
The official results are to be announced on Jan. 15, though preliminary results are expected within a week.
Election observers reported numerous difficulties on Sunday, though many Congolese showed a calm determination to vote. More than 40 million were registered to cast ballots.
Hundreds of polling places opened hours late because they did not have the needed lists of registered voters. Many voters could not find their names on the lists. And there were problems with more than 500 of the electronic voting machines.
Many polls stayed open into the night to allow those waiting in line to cast ballots. At least one Kinshasa polling station didn't manage to open until after the official closing time.
Also, the Kabila government decided at the last minute to bar an estimated 1 million people in two opposition-stronghold cities from voting on Sunday, citing the deadly Ebola outbreak in the eastern part of the country.
Among the 21 candidates, top opposition leaders Martin Fayulu and Felix Tshisekedi are challenging Kabila's preferred successor, former Interior Minister Emmanuel Ramazani Shadary, who is under European Union sanctions for a crackdown on people protesting delays in the election.
The election had been postponed since late 2016, prompting the opposition to charge that Kabila was trying to stay on past his mandate.
At stake is the future of a country that is desperately underdeveloped, with widespread corruption and armed militia groups operating in the east, but also rich in minerals, including those crucial to the world's smartphones and electric cars.
Parole Kamizelo, 31, of Kinshasa, said he was disappointed in the disorganization of the election.
"You cannot call this an election," he said. "This is an electoral comedy."
He said that despite the numerous irregularities reported, "people were determined to vote in masses." Kamizelo said he expects one of the opposition candidates, Fayulu or Tshisikedi, to win "if we take the will of the people into account without cheating."
"If Shadary is elected, it would be with a magic trick," he said.
The government postponed balloting in the cities of Beni and Butembo in the Ebola-stricken east until March, long after Congo's new leader is inaugurated in January, effectively canceling the votes from those two cities.
However, well over 10,000 people lined up in Beni on Sunday to stage their own election, vowing to deliver the results to the electoral commission. People cast paper ballots and sang in Swahili, "Voting is our right and nobody can stop us."