 Saveljić made his debut for FR Yugoslavia in a 3–1 win over Hong Kong on 31 January 1995.He earned 32 caps and scored one goal for the national team, having represented the country at the 1998 FIFA World Cup and UEFA Euro 2000.In August 2017, Saveljić was appointed CEO of the newly founded Girondins de Bordeaux USA, as a result of a partnership between Bordeaux and Washington, D.C.-based club Olney Girls 99.