The court also ordered that Koptsev undergo compulsory psychiatric treatment in prison.
Koptsev was given a 13-year prison sentence in March for attempting to murder nine people at the beginning of the year, but was cleared of race hate charges.
Russia's Supreme Court overturned the lower court's decision in June and ordered a retrial after both Koptsev's lawyers and the prosecutors appealed against the verdict.
Koptsev, who was 20 at the time of the attack, said in August, "I deeply regret what happened and apologize to the victims' relatives for damaging their health."
He also admitted at the time that he had hurt nine people, but said he had not acted out of racial hatred.
In their appeals, Koptsev's lawyers said the defendant was mentally unstable, while prosecutors said a 13-year sentence was insufficient, and pressed for 16 years in a maximum-security prison.
"The defendant shouted anti-Semitic slogans because he was hysterical that day," defense lawyer Roza Saribzhanova said. "He believes in reincarnation and did not want to kill anyone, but wanted to be killed."
But the public prosecutor demanded the defendant be found guilty of attempted murder and fuelling interethnic and religious hatred. "I also ask the court to rule that the defendant undergo psychiatric treatment during his imprisonment."
The court also questioned two medical experts who confirmed previous psychiatric tests that had diagnosed Koptsev with a schizophrenic disorder. The experts concluded that the defendant had been unbalanced at the time of the attack.
"He could not fully control his emotions and behavior, but was able to assess his actions and their significance," doctors said.
On July 31, the Moscow City Court refused a trial by jury for Koptsev.
