At international level, Kovač played for Croatia in five qualifying matches for the 2002 World Cup and scored one goal in Croatia's 4–0 victory away against San Marino. At the final tournament, he appeared as a starting player in all three group matches before Croatia was eliminated from the tournament with a third-place finish in their group. He was also a regular in UEFA Euro 2004 qualifying, making seven appearances and scoring two goals in away matches, the 1–0 winner against Estonia and the opening goal in the team's 3–0 victory over Andorra. He also played the entire three group matches played by the Croatian team at the final Euro 2004 tournament in Portugal and scored the opening goal in the final group match against England. However, Croatia lost the match 4–2 and was once again eliminated from the tournament as the third-placed nation in its group.