[2][3] Savić made his debut for the national team in 1994, during a time of sanctions for Yugoslavia, following All-Star selections in a tournament in Italy.

Holding the record for the highest number of matches played (444), and also being a highly successful scorer (405 goals), he is considered to be among the true legends of Serbian sports.

During his career, from a player in charge of sifting the opposing networks,[clarification needed] he developed into the strongest pillar of Serbia's defense in front of the goal.

In a duel with Montenegro at the 2008 Olympic Games, he was one of the players most responsible for Serbia's triumph when they won the bronze medal that year.

It was announced on 1 June 2010 that Dejan Savić won the national sports award, which includes lifetime monthly fees.