The party headed by Ukrainian President Vladimir Zelensky, the Servant of the People party - named after the sitcom in which he starred before running for, and winning, the presidency last April - took between 42.7 percent and 44.7 percent of the vote in Sunday's legislative elections, according to exit polls.
The tentative result gives Zelensky a significant mandate and puts his party on the verge of an absolute majority in the Rada, or Parliament.
If confirmed, this would be the best result in a parliamentary election for any party since Ukraine obtained independence from the Moscow with the 1991 collapse of the Soviet Union.
Coming in second in the balloting was the pro-Moscow Opposition Platform-For Life party with between 12-13 percent, while European Solidarity, headed by former President Petro Poroshenko, garnered about 8.5 percent.
According to the exit polls, also obtaining seats in Parliament was the Batkivschina party of former Prime Minister Yulia Timoshenko, with about 7.5 percent of the vote.
The big surprise in Sunday's election was the Golos party of rocker Sviatoslav Vakarchuk, which appeared to have exceeded the 5 percent threshold to get seats in the legislature.
In the best scenario for Zelensky, his party and Vakarchuk could unite, thus gaining a majority and forming a government without needing to court Timoshenko, who also aspires to head the government.
With only the exit poll results having been made public so far, Zelensky appeared before reporters at his party headquarters and insisted, as he had done upon voting Sunday morning, that the prime minister should be a technocrat, an economic "guru" and not a politician from the "old school," like Timoshenko.
In addition, he invited Vakarchuk to hold talks with him and his advisers on forming a government.
Meanwhile, Vakarchuk said that the changes in Ukraine should begin in the Rada, where many political forces are opposing both the approval of anti-corruption laws and peace plans for the eastern Donbas region, which was taken over several years ago by pro-Russian forces.
Almost 30 million of Ukraine's 44.8 million voters went to the polls on Sunday for the third time in less than four months after the two presidential rounds, although the participation was less than hoped for.