It wasn't clear what prompted Vladislav Roslyakov, described as a shy loner, to go on the rampage. The attacker also ignited a firebomb in the class and tried to kill himself before being apprehended.
All the victims died of gunshot wounds.
He added that the fourth-year student had aroused no suspicion, saying teachers called him "peaceful".
The Kerch attack was by far the deadliest by a student in Russian Federation, raising questions about school security.
"We have covered many issues on anti-terrorism security".
Over the course of two hours on Friday, thousands of Kerch residents filed past the coffins containing the remains of the first 17 victims to be buried. The director of the college said: "There were lots of corpses, corpses of kids". Russia's National Guard said Thursday that it has now deployed officers and riot police to all schools and colleges in Kerch. Local media reported at least one of the girls had a leg amputated after the attack.
The mass shooting which took place in Crimea on Wednesday is an unfortunate result of globalization and a collective failure to adapt to it, Russian President Vladimir Putin has said. Putin led those present in a moment of silence and some events on his official program were canceled. They also beefed up security at a new 19-kilometre bridge linking the peninsula with Russian Federation, which opened earlier this year.
Roslyakov enrolled at the college in 2015, according to its website.
Guns are tightly restricted in Russian Federation.
"Civilians can own only hunting rifles and smooth-bore shotguns and must undergo significant background checks", AP points out.
But Aksyonov said Roslyakov made the bomb himself and set it off while using a shotgun he recently acquired and 150 cartridges he bought just a few days ago to conduct his deadly shooting spree.
As of Thursday morning, 44 injured in an attack in Kerch remained in hospitals, including 12 in intensive care.
Russia's counter-terrorism agency said the blast was triggered by an unidentified explosive device.
Reuters news agency said the schools and pre-schools were being evacuated in the city after the blast. "This is how powerful the explosion was", she said, saying others had lost lower limbs.
State television suggested Ukrainian agents were to blame.
Around 50 people, the majority of them teenagers, are believed to have been injured.
"We'll have to increase security now that the bridge is here", said one of the mourners, 58-year-old Pavel Yesin, who works for the local weather service.
A student at the college who asked not to give his name told AFP that "I was in a class when I heard shooting on the first floor".
Another student, Yuri Kerpek, told the state RIA Novosti news agency that the shooting went on for about 15 minutes.
AFP journalists in Kerch, a city on the Crimean peninsula annexed by Russian Federation in 2014, saw the college cordoned off by Russia's National Guard, the army and the police.
At least 10 people wounded in a school attack in Crimea will be airlifted to hospitals in Russian Federation, the health minister has said.