Some earlier reports had quoted officials saying it was a gas explosion, but a spokeswoman for the regional gas-distribution company said it had no contract to supply gas to the college.
No group claimed responsibility for that attack, but Russian security forces said it was the work of an Islamist radical.
Mr Aksyonov later told Interfax the death toll had risen to 18.
Raw footage: Emergency vehicles on the scene of an explosion at a vocational college in Crimea that killed at least 17 people. "There are bodies everywhere, children's bodies everywhere ... They blew up everything in the hall, glass was flying", Grebennikova told Crimean media outlets.
An explosive device rigged with metal fragments went off in the canteen of the college, Russian Investigative Committee's spokesperson Svetlana Petrenko said, AP reported.
"They ran up to the second floor with automatic rifles - I don't know with what - and opened doors.and killed everyone they could find", she said.
"According to provisional information, ten people died, and 50 were injured", National Anti-Terror Committee spokesman Andrei Przhedomskikh told official news agency TASS.
Russian news agencies quoted a senior official with Russia's National Guard, a law enforcement agency, as saying that the attack was being treated as terrorism.
"At the moment, there are 13 dead and about 50 wounded, a lot of them teenagers". Ambulances and injured people on stretchers can be seen outside the college.
"The majority of them are teenagers", the committee said in a statement, adding that the metallic device was planted in the school's cafeteria.