The head of the Central Asian country's prison sentencing board, however, said inmates at six prisons had begun a hunger strike to protest poor conditions.
"The situation in the prisons and in the republic is under control and we will not allow any more uprisings of this type," Bakiyev said at a news conference.
"What happened in our prisons was due to corruption within the prison sentencing board," he said, adding that the prison riots were evidence that unnamed "forces" were seeking to destabilise Kyrgyzstan.
"I can assure you they will not succeed," he said.
He said the final death toll from the riots Tuesday was four. Other sources, including an official in the country's prison administration, human rights activists and families of the inmates, said Tuesday that at least 20 people had died.
The violence was apparently sparked by the transfer of a jailed criminal gang leader, Aziz Batukayev, but quickly spread to other jails as inmates used mobile phones to co-ordinate a protest that turned into a wider upheaval against poor prison conditions.
Bakiyev has struggled to impose law and order in Kyrgyzstan since a revolution last March that forced the Central Asian country's former leader, Askar Akayev, to flee. Bakiyev was elected president in July.
For his part, the director of the Kyrgyz prison sentencing board, Kapar Mukeyev, announced that prisoners had gone on hunger strike.
"Actions of disobedience are continuing in six penitentiary colonies and preventive detention centers," Mukeyev told journalists.
"Inmates at these facilities have gone on hunger strike."
Another sentencing board official who asked not to be named said a total of around 3,000 prisoners were taking part in the hunger strike. They were demanding better prison conditions and that the "truth" be told about the revolts on Tuesday.