Kovtun said he would try two quads in his free program at the 2013 Russian Championships. Although he finished fifth on the senior level, he was named in the Russian team to the 2013 European Championships because Russian regulations guaranteed berths only to the top two finishers while a committee had the right to choose the third entry. In his European debut, Kovtun placed seventh in the short program, fourth in the free skate, and fifth overall with a total score of 226.57 points. In the free skate, his fourth combination (3S-2T) was deemed invalid. Kovtun finished seventeenth in his first World Championships, held in London, Ontario, Canada. He was eighth in the men's event at the 2013 World Team Trophy and Team Russia finished fourth.