Rubuta ci gaba don wannan sakin layi - Kovač ya wakilci Croatia a gasar cin kofin duniya biyu, 2002 da 2006, kuma ya kuma halarci gasar zakarun Turai biyu, 2004
da kuma 2008. A gasar cin kofin duniya ta 2006 ya taka leda sosai a tsaron gida, amma bayan ya karbi rawaya ta biyu a kan Japan ya rasa wasan karshe na rukuni da Australia ta hanyar dakatar da shi. Ba tare da Kovač ba, Croatia ta yi gwagwarmaya a cikin tsaro tare da maye gurbinsa Tomas da ke yin wasan kwallon hannu don burin farko na Ostiraliya ta hanyar bugun penariti. Croatia a ƙarshe ta yi wasa 2<unk>2 tare da Ostiraliya amma an fitar da su daga gasar. Tare da Croatia, Leverkusen, da Bayern, Kovač ya kasance abokan aiki tare da babban ɗan'uwansa Niko Kovač. Ya yi ritaya daga tawagar 'yan wasan kasar a cikin kaka na shekara ta 2009, bayan ya zama kyaftin din kungiyar bayan da dan uwansa ya yi ritaya a shekara ta 2008.