Markovits was part of the Hungarian team which won the gold medal in the 1952 tournament. He played six matches and scored three goals.
Four years later he was a member of the Hungarian team which won again the gold medal in the 1956 Olympic tournament. He played six matches and scored at least three goals (not all scorers are known).
At the 1960 Games he won the bronze medal with the Hungarian team. He played four matches and scored one goal.