Croatia's leftist former prime minister was leading in the first round of the presidential election on Sunday, according to an exit poll that puts the conservative incumbent and a right-wing folk singer vying for second place.

The election comes as the Balkan country prepares to take over the EU's rotating presidency next month.

According to the exit poll on Nova TV, Social Democrat Zoran Milanovic garnered 28.69% of the vote followed by 25.63% for incumbent President Kolinda Grabar-Kitarovic.

But close behind with 24.26% was Miroslav Skoro, a right-wing folk singer running as an independent.

The exit poll did not take into account votes from the Croatian diaspora, around 170,000 eligible voters who could ultimately determine who faces the run-off on January 5.

Grabar-Kitarovic, who took on the mostly ceremonial post as Croatia's first female president in 2015, is backed by the establishment HDZ party that has led the country for most of the past three decades. 

During the campaign she struggled to hold on to the party's far-right faction, who drifted towards folk singer-turned-politician Skoro. 

The split on the right carved out a space for centre-left Milanovic to take the lead, though he may face a tougher task in the run-off when the other camp is more united. 

Prime minister from 2011 to 2016, Milanovic was previously derided for his arrogance but has been trying to make a comeback with a promise to make Croatia a "normal" country with an independent judiciary and respect for minorities.

Analysts say a loss for Grabar-Kitarovic could spell trouble in next year's parliamentary elections for Prime Minister Andrej Plenkovic, a moderate in HDZ.

Starting on January 1, his government will be tasked with hosting the EU's presidency for a six-month term, with thorny issues like Brexit and the Western Balkans' membership bids on the agenda. 

Emigration exodus

The campaign was largely light on policy ideas with many candidates instead attacking each other with war-era grievances.

"They stole the space for issues of vital importance for most people's lives, including the young who are leaving in increasing numbers," lamented Matija Horvat, a 27-year-old economist.

The government has struggled to curb an emigration exodus as huge numbers of Croatians pack their bags for better pay and professional opportunities in wealthier EU states. 

Many who leave also cite the culture of nepotism and corruption at home, plus poor public services, as key motivations. 

A total of 3.8 million people were eligible to vote.