Kopitar first played in an international tournament when he participated in the Division I (second level) tournament of the 2003 IIHF World U18 Championships for the Slovenian national junior team. He appeared in five games and recorded three points. The following year he appeared in the 2004 U18 tournament and the 2004 World Junior Championships. Slovenia competed in Division I at both tournaments, one level below the top division. Kopitar scored six goals and eight points in five games during the under-18 tournament and finished second overall for goals scored and third for points, leading Slovenia in both categories; at the World Juniors he had one goal and one assist in five games.