Pungor began his international career in 2004 at the Continental Cup show jumping in Planica , where he reached 80th and 72nd place. Also in the following Continental Cup competitions he did not manage to reach the points. On June 30, 2006 he started for a jumping in Bischofshofen as part of the FIS Cup , but without success. After another Continental Cup season without winning a point, he surprisingly won the gold medal in singles at the Hungarian Championships in 2007 in Kőszeg . A year later he started again at the Hungarian Championships, but in the junior class and won gold again. Despite this success, he ended his international career in the same year due to a lack of measurable success at the international level.