Zelenskiy, who took office in May, has so far been stymied by a parliament dominated by his opponents. He ordered the election for the Verkhovna Rada to be held three months earlier than scheduled to try to get a majority that would support his promised fight against Ukraine's endemic corruption and for other reforms.
His "Servant of the People" party — named after the television comedy in which he played a teacher who unexpectedly becomes president — is supported by 52% of the Ukrainians who intend to vote, according to a survey by the Kiev International Institute of Sociology.
But that edge doesn't necessarily ensure a majority in the legislature. Of the 424 seats to be filled, only 225 of them will be chosen by a national party list. The 199 others are single-mandate seats, whose composition could differ markedly from nationwide sentiment.
A party led by one of Russian President Vladimir Putin's closest associates, tycoon Viktor Medvedchuk, is polling in second place with about 10%, followed by the European Solidarity party of former President Petro Poroshenko, whom Zelenskiy defeated in a landslide in the country's spring presidential election.
Zelenskiy's party intends to continue a pro-Western course toward joining the European Union and NATO, combining this with a package of economic reforms. "The position of the Ukrainian people is movement in the direction of Europe and it will be wrong to reconsider," party leader Dmytro Razumkov told The Associated Press.
The party say it will focus on resuscitating anti-corruption reforms that stalled under Poroshenko. Razumkov says this could be a watershed for Ukraine, bringing in a new political culture of lawmakers interested in reforms rather than using political power for money.
"There are new people who today have completely different basic values than the representatives of the old political elites. This is a new team that Zelenskiy leads to implement new tasks," Razumkov said.
In contrast, Medvedchuk says Ukraine's proper course is to improve its relations with Russia, which plummeted after Russia's 2014 annexation of Crimea and its support for Russia-backed separatists fighting government troops in a war that has killed more than 13,000 people.
"If we do not restore economic pragmatic relations with Russia ... then we have no chance to overcome the economic crisis, which continues and is being aggravated," Medvedchuk told the AP. He proposes that Ukraine grant autonomy to rebel areas in the east and offer amnesty to the separatists. He said Ukraine could get a 25% discount on natural gas imports from Russia if it takes steps that satisfy the Kremlin.
Since Putin is the godfather of Medvedchuk's daughter, his statements likely reflect Kremlin thinking. Medvedchuk once again underlined his ties with the Russian leader when the two met Thursday in St. Petersburg.
"We will work with any political force, including your political force, to restore relations between Russia and Ukraine," Putin said. Razumkov said Zelenskiy's party is ready to negotiate with Russia on mechanisms for conflict resolution and seeks peace in the east, "but not at any cost."
"What Medvedchuk says is not a strategy for returning territories, not a strategy for ending the war," he said. Analyst Volodymyr Fesenko of Ukraine's Penta think tank says the ideas proposed by Medvedchuk are widely perceived as "the restoration of the Russian protectorate over Ukraine."
"Even an attempt to agree on such a scenario will provoke vehement resistance within Ukraine from the side of militant patriots and other political forces. And this can provoke a serious political crisis and even a new Maidan," Fesenko said, referring to the mass protests that drove out the country's Russia-friendly president in 2014.
Medvedchuk also provoked an uproar when a television channel he controls tried to arrange a teleconference with a Russian state channel that is consistently critical of Zelenskiy. Russian TV channels are banned from the air in Ukraine and the teleconference plan was canceled.