Ćurčić was a member of the Yugoslavia national basketball team that participated at the 1953 European Championship in Moscow, the Soviet Union. Over ten tournament games, he averaged 11.0 points per game while shooting 80.4 percent from the field. He was the team-leading scorer and had three games with 20 and more points scored. Ćurčić was a member of the national team at the 1954 FIBA World Championship in Rio de Janeiro, Brazil. Over five tournament games, he averaged 11.4 points per game while shooting 77.1 percent from the field. Ćurčić was a member of the national team at the 1955 European Championship in Budapest, Hungary. Over eleven tournament games, he averaged 11.2 points per game while shooting 72.8 percent from the field. He was the team-leading scorer and had two games with 20 and more points scored. On June 19, 1955, he scored a career-high 26 points in a 66–69 loss to Italy.