Around 12 mutineers had been arrested, Kabila said on Friday appealing for the country to stay calm.
"The population must remain calm and vigilant and ready itself, why not, to resist because I won't allow anyone to try either to stage a coup d'etat or to derail the peace process," said Kabila.
Earlier, renegade presidential guards tried to take over the state radio station in an apparent failed coup attempt.
Information Minister Vital Kamerhe said the situation was now calm and the radio station had been recaptured. He said the coup officers had retreated to a military base within Kinshasa and were surrounded.
"Some officers in the presidential guard took control of the state radio at 2:30 (0130 GMT) this morning, but loyalist soldiers retook control two and a half hours later," government Kamerhe said.
Army major ringleader
The drama started after Major Eric Lenge of the elite unit which guards Kabila took over the airwaves and announced that the country's transitional process was not working and that he was suspending it and taking control himself.
Joseph Kabila took power in 2001
when his father was assassinated
Kamerhe said Lengue then headed to the national electricity company, SNEL, where his forces caused a power cut in Kinshasa that lasted some three hours. President Kabila was safe.
Reliable sources said Lengue is in his 30s, a member of a special presidential guard. They said he had been backed by about 20 supporters.
A UN official said it appeared to be an isolated incident. However, heavy artillery fire was heard in the capital after the attempted coup.
The incident comes days after government troops recaptured the eastern town of Bukavu from dissident soldiers.
The troops had rebelled in a week-long occupation protesting at what the dissidents said was the persecution of their ethnic group.
The revolt in Bukavu exposed the weakness of Kabila's transitional government installed a year ago, which is still struggling to restore central authority across Africa's third-largest country after five years of war.
UN troops have been attacked for
failing to stop the fall of Bukavu
The clashes in the mineral-rich east also raised fears of a wider regional conflict involving Congo and its tiny neighbour Rwanda, which invaded the former Zaire in 1996 and 1998.
Renegade troops attacked four military bases and two television stations in Kinshasa in March in an apparent coup attempt - the first political violence in the city for five years.
Kabila's office blamed members of the personal guard of late dictator Mobutu Sese Seko for those attacks.