Kostitsyn represented Belarus extensively at the under-18 and -20 levels. He first played internationally at the 2000 IIHF World U18 Championships as a fifteen-year-old, but Belarus would struggle in the top division, finishing last. The next year, Kostitsyn competed with Belarus' under-20 team in the 2001 World Junior Ice Hockey Championships' top division. Later that year, having been relegated for the 2001 IIHF World U18 Championships, Kostitsyn returned to record a tournament-leading 14 points in five games within the second-tier to win the Division I championship.