Exit polls suggest the Servant of the People party will have a majority in parliament – but will need a coalition partner to form a government.
Mr Zelensky triumphed in April’s presidential poll – but has been unable to appoint the ministers he wants.
He has pledged to implement radical reforms and tackle rampant corruption.
Speaking outside a polling station after casting his ballot in Kiev earlier on Sunday, Mr Zelensky told the BBC’s Steve Rosenberg that the snap election was “maybe more important than the presidential election”.
What are the results so far?
Five parties look on course to clear the 5% threshold to enter parliament.
Partial official results – with 29% of the vote counted – give President Zelensky’s party 42.1%, with the pro-Russian Opposition Platform – For Life party in second place with 12.7% of the vote. However, Mr Zelensky has ruled out any coalition with it.
Speaking in Kiev after the polls closed, President Zelensky said he was inviting a party led by rock star Svyatoslav Vakarchuk to hold talks on forming a coalition.
“This was my initiative even before the election,” Mr Zelensky said.
Mr Vakarchuk’s Holos (The Voice) party has so far won 6.4% of the vote.
The other two parties projected to enter parliament are former President Petro Poroshenko’s European Solidarity (8.7%) and Batkivshchyna (Fatherland) led by former Prime Minister Yulia Tymoshenko (8.2%).
Mr Zelensky needs support from the Verkhovna Rada, Ukraine’s parliament. The victorious party or coalition will form a government and nominate a prime minister.
The president told our correspondent that the “president, prime minister and parliament have to work together, just to make life happy for Ukraine”.
He said the key issues were investment, democracy and safety.
The comedian president
Mr Zelensky was known for his comic role on TV as a teacher who wins the heart of the nation and becomes president after his expletive-laden rant about politics goes viral.
In reality, his route to the leadership was a bit more conventional than in his show – but only a bit.
After shunning rallies and speeches and openly admitting he didn’t have any strong political views, he scored a landslide victory in April and unseated Mr Poroshenko, a political heavyweight.
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