Competing in his second Olympics, Jurcina represented Slovakia in 2006. He notched one assist and eight penalty minutes in six games. He also skated for Slovakia at the World Championship in 2006, registered three points (2-1-3) and eight penalty minutes in seven games.
In 2007, Jurcina played for Slovakia at the World Championship and recorded one goal and one assist in seven games. He first took to the ice for his country at the 2002 and 2003 World Junior Championships.