Kostitsyn made his second under-20 appearance at the 2002 World Junior Ice Hockey Championships and scored three goals to help Belarus stay in the top division. Later that year, Kostitsyn returned to the top division at the 2002 IIHF World U18 Championships, recording 10 points in eight games and helping lead Belarus to a fifth-place finish. Competing in his third under-20 tournament at the 2003 World Junior Ice Hockey Championships, Kostitsyn recorded two goals and one assist, but was relegated with Belarus to Division-I for 2004. Playing in the second-tier, he notched five goals and 10 points in five games to help Belarus return to the top division in 2005, where he scored five points in his fifth and final World Juniors.