Omark has represented Sweden several times. He made his international debut with the junior team at the 2007 World Junior Championships in his native country, scoring five points in seven games to help Sweden to a fourth-place finish in the tournament. He made his senior international debut at the 2009 IIHF World Championship in Switzerland. Omark recorded ten points in nine games as Sweden captured the bronze medal. He again represented his country at the 2010 IIHF World Championship in Germany, and Sweden won another bronze medal with Omark recording four points.