It was reported guards were taken hostage at some of the facilities.
Heavily armed police and soldiers later entered the prisons of El Oro, Loja, Chimborazo, Cotopaxi, Azuay and Pichincha, and were seen rounding up half-naked inmates in courtyards.
The SNAI said there had been no injuries due to the "incidents".
Mr Izurieta said Fito — who studied law in prison — was a "criminal with extremely dangerous characteristics, whose activities have characteristics of terrorism".
"The search continues… He will be found, he must be found," he said.