State-run news agency TASS reported that most of the victims were students, quoting local ombudswoman Lyudmila Lubina.
Military units were deployed around the college.
Committee spokesman Andrei Przhezdomsky said sappers were inspecting the building for other explosive devices.
A mass shooting on October 17 at a college in Crimea, which Russian Federation annexed in 2014 from Ukraine, left 18 dead and dozens of others wounded. Since the operation to annex the peninsula, there have been no outbreaks of violence there.
Olga Grebennikova, the headmistress of the Kerch technical college where the attack too place was filmed on her mobile phone explaining her perspective of the incident. Its pupils are mostly teenagers.
"A lot of dead bodies, a lot of children's dead bodies".
Softbank shares plummet amid concerns over Saudi ties
The Saudi consulate referred Reuters to authorities in Riyadh, who did not respond to questions about the 15 Saudis. Trump visited the kingdom on his first overseas trip as president and has touted arms sales to Saudi Arabia.
"This is not a terrorist act".
Officials in Crimea say the casualty toll at a vocational school shooting in Kerch now stands at 19 dead and more than 50 wounded, many of them severely. "In the 1st floor they opened rooms and killed everyone inside", she continued.
During the course of the day investigators said they found two explosive devices: one in the college canteen and another in the personal belongings of Roslyakov, whose body was discovered in the library.
It was the greatest loss of life in school violence in Russian Federation since the Beslan terrorist attack by Chechen separatists in 2004, in which 333 people were killed during a three-day siege, many of them children, and hundreds were wounded.
The committee said all the victims have died of gunshot wounds, contrasting with previous statements by other officials saying they had wounds resulting from an explosion. There was no immediate claim of responsibility.
He said he "saw bodies on the floor" and the walls were "charred" when police escorted him out of the building.
Facing a crowd of angry parents, some of whom still did not know where their children were, Aksyonov said authorities were seeking to establish the gunman's motives: "What pushed this non-person to do this, I don't know".