Kremlin spokesperson Dmitry Peskov said Wednesday that the possibility that this was a terror attack "is being considered".
Images circulating on social media allegedly show Roslyakov wearing a similar T-shirt to Eric Harris, one of the two killers responsible for the 1999 Columbine High School massacre in the US.
His mother, a nurse, was helping to treat victims at a local hospital after the shootings, yet unaware that her son was accused of the rampage and was already dead.
Yet Russian news media, however, reported that at least some of the victims died in an attack by an unidentified gunman or gunmen. Kerch is the point on the peninsula where a bridge linking Crimea to Russian Federation makes landfall on the Crimean side.
Russia's top investigative agency says an explosive device rigged with metal fragments has killed 13 people at a college in Crimea.
AP points out that school shootings are rare in Russian Federation, where gun ownership is tightly restricted. Roslyakov received a permission to own a shotgun and bought 150 cartridges just a few days ago, according to local officials. It was not immediately clear if the alleged attacker had detonated the explosive device. Explosives experts were inspecting the college building for other possible bombs, according to Anti-Terrorism Committee spokesman Andrei Przhezdomsky.
Several witnesses spoke of a gunman or gunmen and some mentioned a powerful explosion.More news: Andrew Benintendi is at Fault for Red Sox's 5th-Inning Meltdown
Investigators, however, later identified the attacker as 18-year-old Vladislav Roslyakov, a fourth-year whose body was found "with a gunshot wound" on the premises.
Crimean leader Sergei Aksyonov said on Facebook he had gone to the scene and "all the necessary services are working at the scene of the incident". He said he looked out and saw a young man with a rifle shooting at people.
Russian President Vladimir Putin, at a meeting in the southern Russian resort of Sochi with his Egyptian counterpart, declared a moment's silence for the victims. 'I locked the door, hoping he wouldn't hear me, ' he told the Komsomolskaya Pravda newspaper.
It also said that the suspect shot himself and his body had been found inside the college.
Crimea's regional chief, Sergei Aksyonov, told the state news channel Rossiya-24 that 53 people were wounded in the Kerch attack, 12 of whom are now in serious condition.
Olga Grebennikova, the college's director, described a scene of bloodshed at the college, which provides vocational training.
Russian authorities initially put out conflicting versions of what happened at the technical college in Kerch, on the peninsula annexed from Ukraine in 2014.