Džomba was first called up to play for the Croatian national team in 1997 by head coach Josip Glavaš. at the 1997 World Championship in Japan. Croatia finished in 13th place at the tournament being knocked out in the 16th round by Spain. A month later, Džomba was selected for the Mediterranean Games in Bari by new head coach Ilija Piljević. Croatia reached the finals and defeated Italy 21:20. Džomba won his first gold medal for the national team.