He made his debut on 17 June 1964 against Romania and would go on to earn 85 caps (the most in the history of the Yugoslav national team) and score 23 goals.
He made his debut on 17 June 1964 in a 2--1 defeat against Romania at the JNA Stadium in Belgrade. Džajić would go on to earn 85 caps (the most in the history of the Yugoslav national team) and score 23 goals.