Voters in Croatia are heading to the polls to elect their next president in a close race where the conservative incumbent is expected to face a serious challenge from a former prime minister.

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

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The vote comes as the EU's newest member is struggling with corruption, a lacklustre economy and a big exodus of its people seeking better opportunities abroad.

Centre-right incumbent, Kolinda Grabar-Kitarovic, is campaigning on a "real Croatia" ticket, and Zoran Milanovic, a former Social Democratic prime minister, 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.

However, other analysts predict a slight advantage to the incumbent president, who is trying to unite a fractured right wing.

"I believe that she has somewhat bigger chances as the Croatian electorate is generally slightly right-leaning. In any case, this election is a kind of a preliminary stage for the parliamentary election later this year," political analyst Zarko Puhovski told Reuters news agency.

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

Dominating in cities, Milanovic led the first round with 29.6 percent of the vote, thanks in part to the split among the right wing. Kolinda Grabar-Kitarovic gathered 26.7 percent.

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

Polling stations opened at 7am (6:00 GMT) on Sunday and will close 12 hours later, with first results expected approximately 19:00 GMT.

'Croatia that unifies'

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

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

Unity, patriotism and references to the 1990s independence war, which remains an emotive issue, were the key points of her re-election bid.

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

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

"There is no 'real Croatia'... rather a Croatian republic for all, equal citizens," the 53-year-old told a campaign rally in his native Zagreb.

Accelerated exodus

Presenting herself as the "woman of the people" with humble farming roots, Grabar-Kitarovic is well known for stunts such as singing in public, which her critics deride as embarrassing.

She has also come under fire for downplaying the crimes committed by the pro-Nazi Ustasha regime that ruled the short-lived Independent State of Croatia during World War II.

Meanwhile, Milanovic is trying to make a political comeback and throw off a reputation as arrogant and elitist.

He ran his election campaign on promises that he would fight corruption he said had intensified since he left power and the conservatives took over.

A prime minister from 2011 until 2016, he was welcomed at the time of assuming office as a bright, young politician clean of the corruption tainting the rival HDZ.

But the excitement waned after his government failed to push through much-needed reforms.

The conservatives say Milanovic's government ran poor economic policies that caused public debt to pile up.

The ruling HDZ hopes to keep Grabar-Kitarovic in office during the country's EU presidency where four main issues are likely to dominate - the bloc's relationship with the UK after Brexit, the membership bids of Western Balkan states, climate change, and the bloc's budget framework for the next decade.

Croatia joined the EU in 2013 but its economy, strongly reliant on tourism on its Adriatic coast, remains one of the bloc's weakest.

The EU's open borders also accelerated the exodus of Croatians seeking better pay in wealthier member states.

"Our youngsters are leaving, that is the biggest problem" while politicians are only "insulting each other", Stjepan Golub, a 70-year-old man from Zagreb, told AFP.