Ukraine's President, Viktor Yushchenko, has demanded an urgent investigation into the delays in the vote counting of Sunday's early parliamentary election.
The Russia-leaning party of Mr Yanukovych has a narrow lead
This came after partial results from eastern and southern Ukraine gave the Russia-leaning party of Prime Minister Victor Yanukovych a narrow lead.
However, the combined total of Mr Yushchenko and the opposition leader, Yulia Tymoshenko, is larger.
These pro-Western parties have said they plan to form a coalition.
But their slim lead has diminished as late votes come in, while Mr Yanukovych has had steady gains.
There is also a possibility that he could form a coalition with three smaller parties.
Earlier, Europe's main election-monitoring body, the Organisation for Security and Co-operation in Europe, said the elections had met international standards.
In a televised address Mr Yushchenko warned that those who commit fraud will be punished:
"I am concerned at the delayed vote count in Ukraine's eastern and southern regions, namely in Donetsk, Lugansk and Odessa regions and in the autonomous republic of Crimea," he said.
Ms Tymoshenko says she wants to form a new coalition government with President Yushchenko's party - an old ally from the 2004 Orange Revolution.
But Mr Yanukovych refuses to accept defeat in the poll and earlier thousands of supporters of his Regions Party held a rally on Kiev's main Independence Square.
"This significant support from the Ukrainian people... gives carte blanche to the Party of Regions to form a new, successful government," Mr Yanukovych said.
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.
In the lead
With 90% of the votes counted, Mr Yanukovych's Party of Regions (PR) was leading with 33.49%, the electoral commission said.
The Yulia Tymoshenko block (BYT) was a close second with 31.26%, while Mr Yushchenko's Our Ukraine-People's Self Defence (NUNS) trailed in the third place with 14.55%.
Security forces have been ordered to investigate delays in the count
This means that combined votes for the Orange parties may give them only a very slim majority in the 450-member parliament.
The BBC's Helen Fawkes in Kiev says this result could lead to more political deadlock.
Ms Tymoshenko says she will meet the president on Tuesday to discuss forming a pro-Western governing coalition.
On Monday, Ms 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.
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.