People attend New Year's eve celebration in Fuzine, Croatia, on Dec. 31, 2019. Photo:Xinhua

Croatians went to the polls on Sunday to elect a new president in an uncertain vote where the conservative incumbent - trying to unite a fractured right wing - faces a serious challenge from a leftist former prime minister.

Some 3.8 million people are eligible to vote in a poll that is being held just days after Croatia took over the European Union's helm for a six-month period, which will be dominated by Brexit and the bloc's enlargement. 

At the same time, the EU's newest member is struggling with a mass exodus of its people, corruption and a lackluster economy at home.

Center-right incumbent, Kolinda Grabar-Kitarovic, is campaigning on a "real Croatia" ticket, and Zoran Milanovic, a former Social Democratic premier, is promising a "normal" liberal democracy of equal citizens.

The outcome of the vote for the largely ceremonial post is uncertain, with the latest survey by Ipsos agency giving Milanovic a three-percentage-point lead over Grabar-Kitarovic.

The latter, backed by the ruling HDZ party, will have to lure back hard-liners who voted for a nationalist folk singer in the election's first round in December.

Dominating in cities, Milanovic led the first round with around a third of the vote, thanks in part to that split among the right-wingers.

Analysts said the first-round results showed an increase in support for hard-liners, a trend seen in other European countries such as Poland or Hungary.

If Grabar-Kitarovic fails to win the presidency, it would deal a heavy blow to the HDZ, whose moderate Prime Minister Andrej Plenkovic faces parliamentary elections later this year.

"I am a Croatia that unifies," Grabar-Kitarovic, 51, said during a TV election debate with her rival.

Unity, patriotism and references to the 1990s independence war that remains an emotive issue, were the key points of her reelection bid.

"We should come together as in 1990," before the country declared independence from Yugoslavia, Croatia's first female president told her supporters in Zagreb.

Meanwhile, Milanovic insisted that the "wars are over" and Croatia should now fight for its place in Europe.