Muršak was chosen to compete on the Slovenia national junior team in the 2008 World Junior Ice Hockey Championships (Division I) in Latvia, where he scored one goal and two assists and was named the best forward of the tournament. He made his debut for the Slovenian senior team at the 2010 Division I Championships, held in the Slovenian capital, Ljubljana. In 2014, Muršak represented Slovenia at their first appearance at the Olympics. Muršak also represented Slovenia at the 2018 Winter Olympics in Pyeonchang, most notably coming on as a substitute in the last minutes of the game against USA, and scoring two late goals to win them the game.