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 parliament 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.
The vote to elect mayors, local and regional councils is not being held on the Crimea peninsula annexed by Russia in 2014 or in the self-proclaimed Donetsk and Lugansk People’s Republics in eastern Ukraine.
A poll published this month showed that just 17 percent of voters planned to cast ballots for the Servant of the People party.
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.
– ‘People we trust’ -In a separate opinion poll, some 60 percent of voters said they planned to cast their ballots for one of several Russia-friendly parties.
“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 first held in Ukraine since the start of the coronavirus pandemic and 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, is expected to win easily.
But he was not able to vote 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.
Seventy-four-year-old Viktor, who also declined to give his last name, said he voted for a candidate from Zelensky’s party to become mayor.
“We must support the president,” he said.
Polling stations opened at 0600 GMT and close at 1800 GMT. Final results are expected in several days.
AFP