Early exit polls showed that Ukraine's President Volodymyr Zelensky has suffered a setback in Sunday's local elections, while his pro-Russian and pro-European rivals are leading in most of the country's major cities.

In nine major cities and regional centres across the country where the polls were held, no presidential party candidate was elected mayor -- not even in Zelensky's hometown.

His party Servant of the People won the elections to municipal councils in two large cities in the centre of Ukraine, but in the other seven it most often placed third or fourth, according to two polls.

The local elections were seen as a test for Zelensky, whose popularity has suffered in the year-and-a-half since he came unexpectedly to power.

Zelensky, a former comedian with no political experience, won a landslide victory in a 2019 presidential election promising to root out corruption and end a war with Russian-backed separatists in the east.

His newly created Servant of the People party won an outright majority in a parliamentary election last year, a record win in the former Soviet republic of around 40 million people.

But in the absence of tangible results, Zelensky's popularity and that of his party has been on the decline.

"His party is losing political leadership in almost all regions," analyst Mykola Davydiuk told AFP.

"This is a very heavy blow for him," Davydiuk said, adding that it could mean a change of government and even early parliamentary elections.

Voter turnout reached just 36 percent, according to the Ukrainian election watchdog Opora, while in previous local elections five years ago it was almost 47 percent.

"Unlike some of our neighbours, we do have a great luxury -- free elections," Zelensky said on his Facebook page after the exit polls, alluding to neighbouring Russia and Belarus.

A poll published days before the vote showed that just 17 percent of voters planned to cast ballots for the Servant of the People party.

Sunday's vote is the first held in Ukraine since the start of the coronavirus pandemic
Sunday's vote is the first held in Ukraine since the start of the coronavirus pandemic AFP / Sergei SUPINSKY

In close second was a pro-Russian party, Opposition Platform - For Life, with 14 percent, followed by the pro-Western European Solidarity aligned with former leader Petro Poroshenko with 13 percent.

In areas of the eastern Donetsk and Lugansk regions that are still controlled by Kiev, only 10 percent of voters planned to vote for Zelensky's party.

The vote to elect mayors, local and regional councils did not extend to the Crimea peninsula annexed by Russia in 2014 or the self-proclaimed Donetsk and Lugansk People's Republics in eastern Ukraine.

"We will see the figures," Zelensky said Sunday in response to a question about his party's popularity.

"It's important that we elect people who we trust," he said after casting his vote. "These are local elections, it's important what these people are able to do in their localites."

Sunday's vote is the first held in Ukraine since the start of the coronavirus pandemic. In polling stations equipped with disinfectant dispensers, election officials wore masks and gloves.

Voters were asked to maintain social distance, wear a mask and have their temperature taken before casting their vote.

In the capital Kiev, acting mayor and former boxing champion Vitali Klitschko has the best chance to win the mayoral election with more than 45% of votes, according to two exit polls.

If the numbers are confirmed and he does not receive more than 50%, the second round is expected on November 15.

Klitschko was not able to vote himself because he was self-isolating after testing positive for coronavirus.

At a polling station in the Pechersk district in Kiev, more than 30 people had lined up to vote.

"I want to return to the time before 2014, before these reformers who are dragging us towards Europe came to power," Inna, a retiree, who said she voted for pro-Russian party, told AFP.

"What have we got since then? War, devastation, poverty," she said on the condition that she withhold her last name.

Final results are expected in three to five days, according to the election commission.