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His likely main rival among the eight contenders for the largely ceremonial post is Dragan Primorac, backed by the ruling conservative HDZ party.
The election comes as the European Union and NATO member country of 3.8 million people struggles with biting inflation, widespread corruption and a labour shortage.
Milanovic, backed by the left-wing Social Democrats party, is supported by 37 percent of the electorate while Primorac has 20 percent, according to an opinion poll released Friday.
But as none of the candidates are expected to garner more than 50 percent of the vote to win outright, the new head of state is likely to be chosen in a runoff in two weeks.