Ukraine's opposition leader Yulia Tymoshenko says she wants to form a new coalition government following Sunday's closely fought parliamentary election.
Mrs Tymoshenko is now gunning to replace Mr Yanukovych
She aims to join forces with President Viktor Yushchenko's party - an old ally from the 2004 Orange Revolution.
Partial results show Mrs Tymoshenko's bloc is narrowly trailing arch-rival Prime Minister Viktor Yanukovych, who refuses to accept defeat in the poll.
But combined votes for the two Orange parties give them a slim advantage.
The snap election was the third national poll in three years.
It was called in an attempt to resolve a long-running power struggle between West-leaning Mr Yushchenko and Mr Yanukovych, who is viewed as being closer to Russia.
Just over 60% of the 37.5m eligible voters cast their ballots, Ukraine's electoral commission said.
Monitors from the Organisation for Security and Cooperation in Europe described the vote as "open and competitive".
They said it was "mostly in line with... standards for democratic elections".
In the lead
With nearly 80% of the votes counted, Mr Yanukovych's Party of Regions (PR) was leading with 32.45%, the electoral commission said.
The Yulia Tymoshenko block (BYT) was a close second with 31.91%, while Mr Yushchenko's Our Ukraine-People's Self Defence (NUNS) trailed in the third place with 15%.
The Tymoshenko bloc and the NUNS are now widely expected to form a governing coalition, and the process could formally begin when Mrs Tymoshenko meets the president on Tuesday.
On Monday, Mrs Tymoshenko told reporters: "I believe no-one can diminish or deny the victory Ukraine has scored.
"Everything will work out. In a matter of weeks we will hold our first government news conference."
The NUNS struck a last-minute agreement before the election to form a coalition with the Tymoshenko bloc.
Under the deal, Ms Tymoshenko would return to the post she was sacked from in 2005.
Rival rally plans
As results were coming in, Mr Yanukovych refused to yield ground, saying his party had won the election.
"This significant support from the Ukrainian people... gives carte blanche to the Party of Regions to form a new, successful government," he said.
Mr Yanukovych says his party will be forming a new government
Mr Yanukovych later addressed his supporters at a rally in Kiev, saying that his party would form "a government of national unity".
Exit polls had suggested the PR would emerge as the biggest party in the 450-member parliament but would not have enough seats to prevent the two Orange parties from forming a government.
The official results - due later on Monday - are likely to be challenged in courts, correspondents say.
The coalition horse-trading after last year's parliamentary elections took months and plunged Ukraine into political turmoil which helped trigger the latest snap poll.
Mr Yanukovych's power base is in the largely Russian-speaking south-east, while the Orange parties enjoy support in western and central regions.
History of infighting
Mr Yushchenko and Ms Tymoshenko led the 2004 pro-democracy street protests - dubbed the Orange Revolution - that swept them both to power.
The president made Ms Tymoshenko his prime minister in 2005, but their government was brought down by infighting.
Mr Yushchenko and Mr Yanukovych were rivals in the 2004 presidential poll.
Mr Yanukovych won the initial poll, but the result was annulled over claims of mass vote rigging.
Orange-clad campaigners won a peaceful campaign for fresh elections and Mr Yushchenko triumphed in the re-run.
But Mr Yanukovych made a comeback as prime minister in March 2006 and the two enemies grudgingly shared power.
The EU, the US and Russia are all vying for influence in Ukraine, which straddles key Russian gas export routes to energy-hungry EU nations.