Kovačević is a gold medallist of the 2011 European Championship. In 2011, Kovačević was granted an award by the Olympic Committee of Serbia for the best young athlete. He was a member of the national team at the Olympic Games London 2012. On 19 July 2015, the Serbian national volleyball team reached the final of the World League, but eventually lost to France (0–3), and achieved silver medals. He was named "MVP" of the 2019 European Championship where Serbia won a gold medal.