President Volodymyr Zelensky is set to become the first Ukrainian leader since the fall of communism to command an overall majority in parliament.
Servant of the People, the party named after the TV sitcom that made him famous, has won 43.1% of the vote with almost 94% of results counted.
The party is on course to win 253 of parliament's 450 seats.
A decisive win for Mr Zelensky's party will make it easier for him to push through reforms and tackle corruption.
It will also be the best result by any party in Ukraine's post-1991 history.
Since he triumphed in April's presidential poll, Mr Zelensky, 41, has been unable to appoint the ministers he wants.
On Sunday, 424 seats in the parliament, the Verkhovna Rada, were contested. Those seats not included represent the war-torn Donbas region and Crimea, which was annexed from Ukraine by Russia in 2014.
Speaking outside a polling station after casting his ballot in Kiev on Sunday, Mr Zelensky told the BBC's Steve Rosenberg the snap election was "maybe more important than the presidential election".
His party was on course to win 124 seats in the party list vote, which is decided by proportional representation. It was also set to win a further 129 seats in single-seat races that make up half the vote.
What are the latest results?
Five parties look on course to clear the 5% threshold to enter parliament, with the pro-Russian Opposition Platform-For Life party in second place with 13%.
The Holos (Voice) party, seen as a possible coalition partner for Mr Zelensky should he need one, has so far won 5.8% of the vote.
The other two parties projected to enter parliament are former President Petro Poroshenko's European Solidarity (8.1%) and Batkivshchyna (Fatherland) led by former Prime Minister Yulia Tymoshenko (8.2%).
The victorious party or coalition will form a government and nominate a prime minister.
What powers does Ukraine's parliament have?
- The president is in charge of foreign policy, defence and security but parliament handles nearly all other policy areas, notably the economy and social welfare
- A majority of MPs propose a prime minister-designate to the president
- The PM, if confirmed by president and parliament, names members of the government
- Parliament confirms or rejects the government team, or indeed individual ministers, and can impeach the president
- MPs have a veto on key state posts such as national security service chief, central bank chief and chief prosecutor
The president told our correspondent 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 did not have any strong political views, he scored a landslide victory in April and unseated Mr Poroshenko, a political heavyweight.
The election was widely expected to give Mr Zelensky a greater mandate for reform, sweeping aside the old guard and bringing new faces to parliament.
One of the candidates for Servant of the People, for example, is Zhan Beleniuk, a 28-year-old Olympic wrestler who has now become Ukraine's first mixed race MP.