A Montenegro international since its inception, Marković participated at the 2008 European Championship in the nation's debut appearance in major tournaments. He was later omitted from the national team for the 2013 World Championship, before switching allegiance to Qatar. After being cleared to play, Marković made his debut for the Qatar national team at the 2015 World Championship, helping them finish as runners-up. He also won the gold medal at the 2016 Asian Championship and took part in the 2016 Summer Olympics.