Interior Minister Marco Antonio Villeda said he was prepared to talk to the prisoners but would not agree to their demands.
According to a statement from the Ministry of the Interior, the prisoners' rebellion is due to the removal of privileges from certain gang leaders.
"In Guatemala, we do not negotiate with terrorists or with organized crime," the statement said.
Police have been deployed around the three prisons, but there are no reports of injuries or deaths.
Last October, 20 gang members escaped from several prisons in the country. In August of the same year, two guards were taken hostage after a riot at the Gaviotas prison in the capital, Guatemala City.
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