At his first major international competition, Zorko finished sixth in the men's 3000 metres race at the 1989 IAAF World Indoor Championships. In 1990, he won his first major medal, winning bronze at the European Indoor Championships in Glasgow. After the breakup of Yugoslavia, Zorko began specializing in middle-distance disciplines, and eventually found his talent in the 1500 metres. In 1992, Zorko won the first international medal for the newly independent Croatia, winning a bronze medal at the 1992 European Indoor Athletics Championships. A year later he won the bronze medal for the men's 1500 metres at the 1993 IAAF World Indoor Championships, finishing only 0.39 seconds behind winner Marcus O'Sullivan. Next year, Zorko finished second in the 1500 at the 1994 European Athletics Indoor Championships, and third at the 1994 European Championships in Athletics.