Slavnić played in 179 games with the senior Yugoslavian national team, and scored 1,465 points. He's one of the rare players with gold medals from the Summer Olympic Games, the FIBA World Cup, and the FIBA EuroBasket. He won three EuroBasket titles, 1973 in Barcelona, 1975 in Belgrade, and 1977 in Liege. He won the gold at the FIBA World Cup, in Manila in 1978, and Olympic gold, in Moscow in 1980.