Capped 50 times by Yugoslavia between 1959 and 1966, Durković excelled as a 22-year-old at the first UEFA European Championship, offering defensive solidity and attacking penetration at right-back. Although Yugoslavia finished second in France, Durković won a gold medal at the Rome Olympics the following September. He also wore the number two shirt at the 1962 FIFA World Cup in Chile and was an ever-present as Yugoslavia eliminated former winners Uruguay and West Germany and finished fourth.