Nyora kuenderera mberi kweiyi ndima - Kovač akamiririra Croatia mumakwikwi maviri eWorld Cup, 2002 na2006, uye akapindawo mumakwikwi maviri eEuropean Championship, 2004
uye 2008. PaWorld Cup 2006 akatamba zvakanaka mukudzivirira, zvisinei mushure mekutora yero yechipiri kurwisa Japan akarasikirwa nemutambo wekupedzisira weboka neAustralia kuburikidza nekumiswa. Pasina Kovač, Croatia yakatambura mukuzvidzivirira nemutsivi wake Tomas achiita handball yeAustralia yekutanga chinangwa kuburikidza nepenalty kick. Croatia pakupedzisira yakaita 2<unk>2 neAustralia asi yakabviswa mumutambo. NeCroatia, Leverkusen, uye Bayern, Kovač aive vatambi pamwe nemukoma wake mukuru Niko Kovač. Akasiya chikwata chenyika mukudonha kwa2009, ave kaputeni wechikwata mushure mekurega basa kwemukoma wake muna2008.