The Party of Regions has more than 36%, and the opposition party of Yulia Tymoshenko, who is in jail, has just over 21%, with one-third of party list votes counted.
It appears Viktor Yanukovych’s party is also ahead in single mandate districts, which form half of all the seats.
Western governments have condemned the jailing of Yulia Tymoshenko.
Yulia Tymoshenko leads a coalition of opposition groups – the United Opposition Fatherland bloc. She was given a seven-year jail sentence last year for abuse of power, and voted from her prison cell.
Her bloc says its own parallel vote count confirms that Viktor Yanukovych’s party is in the lead, but with a smaller percentage of votes than the party claims.
The complicated electoral system means a final result is some way off.
Thousands of observers were in Ukraine for the vote, whichViktor Yanukovych hopes will boost his democratic credentials.
His bitter rivalry with Yulia Tymoshenko dates back to the 2004 Orange Revolution, in which Tymoshenko and her allies established a pro-Western government, overturning Viktor Yanukovych’s victory in an election widely condemned as rigged.
Since his dramatic political comeback Viktor Yanukovych has forged closer relations with Moscow, Ukraine’s former master in the Soviet era.
The regional security organization OSCE is expected to give its verdict on Sunday’s election at a news conference at 14:30 local time.
Correspondents say the signs are that the Party of Regions will get a simple majority in the 450-member parliament.
Officials said the election had passed off smoothly, with a turnout of some 45%, about average for Ukraine.
Early results indicated the Communists – traditional allies of Viktor Yanukovych – were in third place with about 15%.
The new party of world heavyweight boxing champion Vitali Klitschko, called Udar (Punch), was on about 13%.
The ultra-nationalist Svoboda (Freedom) party was also poised to surpass the 5% threshold necessary to get seats in parliament. It was polling 8%, according to the early results.
Party of Regions MP Borys Kolesnikov, a deputy prime minister, said his party was likely to dominate the single-seat constituencies.
“There are 225 single-seat constituencies and we see our candidates winning two-thirds of them,” he said.
And Prime Minister Mykola Azarov said “we are expecting that the Party of Regions will take a majority in the new parliament”.
After casting his vote in the capital, Kiev, Vitali Klitschko said he was “going to parliament to fight”.
He listed his “five key punches” as corruption, indifference of the authorities, lack of local governance, inequality and poverty.
There were 3,500 accredited foreign observers, including more than 600 from the Organization for Security and Co-operation in Europe (OSCE).
Earlier, Western officials expressed concerns over campaigning.
In a New York Times editorial, US Secretary of State Hillary Clinton and EU foreign policy chief Catherine Ashton cited “worrying trends” in the interim election report from the OSCE (of which Ukraine is due to take over the rotating chair in January).
These included government resources being used to favor ruling-party candidates, media restrictions, vote-buying and lack of transparency on the electoral commissions.
Opposition supporters say Yulia Tymoshenko was prosecuted and imprisoned last year in order to prevent her running in the election.
The EU indefinitely postponed its association agreement, including a free trade pact, after the jailing.
Viktor Yanukovych, who has been president for three years and faces re-election in 2015, has rejected calls to free his rival. He says she was sentenced by an independent court.
Ukraine, with a population of 46 million, has been hit by the global economic downturn and unpopular pension and tax policies.
The Party of Regions recently attempted to assuage public opinion by boosting public-sector salaries and pensions.
But the reforms exacerbated a $2 billion budget deficit and called into question the likelihood of securing IMF lending, correspondents say.
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