News outlets identified the alleged attacker Roslyakov as a fourth-year student at the Kerch Polytechnic College.
Vladislav Roslyakov, 18, killed 20 students in the Moscow-annexed peninsula college before killing himself.
Another witness, who gave his name as Sergei and works near the college, said in a video on the Kerch.tv website that he heard "a bang and shots". "He could not, in my view, have carried out such prepared events alone".
The investigators cited CCTTV footage showing that the man opened fire on people and later killed himself.
The Russian government said it was treating the incident an attack, and bomb experts, armoured vehicles and personnel were sent to the school to secure and investigate the surrounding areas. The motives of the killer are unclear although top Crimean officials said that authorities suspect he had an accomplice who helped him plot the attack. The attack reportedly began with an explosion, followed by additional blasts and then gunfire, according to Reuters.
Local media reported that the explosion happened in the cafetaria, where an improvised explosive device (IED) allegedly went off.
Initially, emergency officials said an explosive device went off at the college's canteen and was rigged with shrapnel.
Russian Defence Minister Sergei Shoigu said four military planes were ready to evacuate casualties for medical treatment, the Interfax news agency reported. "This is how powerful the explosion was", she said, saying others had lost lower limbs.
"He didn't want to live" because of it, said the girl, who broke up with Roslyakov at an unspecified time before the killing.
"When we all ran out into the corridor, there were others running and shouting that some guy with a machine gun was randomly shooting everyone in turn". "The gunman had a hunting gun", Crimean official Igor Mikhailichenko said.
Over the past few years, Russian security agencies have arrested several Ukrainians accused of plotting terror attacks in Crimea, but no attacks have occurred.
The aftermath of the shooting, however, is also unfolding against Crimea's unusual political backdrop.
Crimea - a peninsula south of Ukraine, which is surrounded by the Black Sea and the Sea of Azov - was annexed by Russian Federation from Ukraine in 2014.
Russian Federation has seen several violent attacks by students in recent years, but none of them were even remotely as brutal as the Kerch rampage.
Verkhovna Rada of Ukraine deputy (Petro Poroshenko Bloc faction) and Chairman of the Mejlis of the Crimean Tatars Refat Chubarov has said Russian Federation will use the tragedy at the Kerch technical school in occupied Crimea to pressure those not loyal to the Kremlin regime, including Crimean Tatars.
The school attack in Kerch was the greatest loss of life in school violence in Russian Federation since the Beslan 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.
Aksyonov, the regional leader in Crimea, said the gunman had been described as a shy boy who had no conflicts. On Thursday, armed riot police were temporarily deployed to guard all schools on the peninsula.
"Currently we know of 13 dead and around 50 injured", Investigative Committee spokeswoman Svetlana Petrenko said in televised comments.
Speaking at an global policy conference, Putin compared Roslyakov's assault to the numerous school shootings in the United States.
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