"The motives and theories of this tragedy are thoroughly investigated", Putin said.
The technical college provides vocational training to teenage pupils.
He entered the college in 2015 and got a gun permit and bought a rifle and 150 rounds of ammunition several days before the shooting, 112 reported.
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 also said he might not have been acting alone and it was looking for other possible participants.
Russian media reported that an unidentified gunman or gunmen attacked the college.
The Russian Investigative Committee confirmed that on its website on October 17 that Roslyakov's body had been found in one of the classrooms of the college. "It's a mass killing committed by one scumbag", Aksyonov said earlier on state television. He didn't name the man, saying only that he was a local resident.
"Started running and throwing explosive devices, bombing everywhere", Grebennikova said at a scene on October 17.
Another student, Yuri Kerpek, told the state RIA Novosti news agency that the shooting went on for about 15 minutes. Explosives experts inspected the college building for other possible bombs, according to Anti-Terrorism Committee spokesman Andrei Przhezdomsky.
Investigators said the explosive device went off in the college's canteen and that it was "packed with metal objects". She said most of the victims were students and more than 40 people were injured as a result of the explosion.
Kremlin spokesperson Dmitry Peskov said Wednesday that the possibility that this was a terror attack "is being considered". He did not elaborate. Fifty-three people were wounded, including 12 in serious condition, Crimean authorities said.
The TASS news agency cited Russia's National Anti-terrorism Committee as saying the suspect's body has been found inside the college.
Around 20 people have been rushed to hospital by paramedics and doctors are expected around 50 more wounded.
The head of Crimea, Sergei Aksyonov, and Russian health minister Veronika Skvortsova have travelled to the area in order to support the injured.
Russian Federation annexed Ukraine's Crimea region in 2014, prompting global condemnation and Western sanctions.
Reuters news agency said the schools and pre-schools were being evacuated in the city after the blast.