Rubuta ci gaba don wannan sakin layi - A matakin kasa da kasa, Kovač ya taka leda a Croatia a wasanni biyar na gasar cin kofin duniya ta 2002 kuma ya zira kwallaye daya a wasan Croatia na 4 - 0 da San Marino. A wasan karshe, ya bayyana a matsayin dan wasa na farko a duka wasannin rukuni uku kafin Croatia ta fita daga gasar tare da kammala na uku a rukuninsu. Ya kuma kasance na yau da kullun a cikin cancantar UEFA Euro 2004, yana yin wasanni bakwai kuma ya zira kwallaye biyu a wasannin waje, nasara 1<unk>0 da Estonia da kuma ƙwallon buɗewa a nasarar 3<unk>0 da ƙungiyar ta yi a kan Andorra. Ya kuma buga dukkan wasannin rukuni uku da kungiyar Croatia ta buga a wasan karshe na Euro 2004
a Portugal kuma ya zura kwallaye a wasan farko a wasan karshe da Ingila. Koyaya, Croatia ta rasa wasan 4<unk>2 kuma an sake fitar da ita daga gasar a matsayin ƙasa ta uku a rukunin ta.