At least 10,000 opposition supporters are holding a rally in the Ukrainian capital Kiev, accusing the government of rigging Sunday's presidential poll.
Opposition supporters filled the centre of Kiev overnight
With about 75% of the votes counted, the pro-Russian Prime Minister Viktor Yanukovych is officially just over 1% ahead of his rival Viktor Yushchenko.
Mr Yushchenko's supporters say they do not believe the official turnout figure of 96% in eastern Ukraine.
Exit polls had shown Mr Yushchenko, a pro-Western liberal, in the lead.
Sunday's vote was a second round run-off after a bitter dispute over the first round results.
"I believe in my victory but the government... has staged total fraud in the elections in the (eastern) Donetsk and Lugansk regions," Mr Yushchenko said in a statement.
In the first round the eastern regions showed strong support for Mr Yanukovych - a former governor of Donetsk.
"I do not trust the Central Electoral Commission," he added.
Imprisoned twice in his youth
Former governor of industrial Donetsk region
Raised pensions and public sector pay before election
Would make Russian second official language and allow dual citizenship
An economist and former central banker
Has an American wife
Promises to fight corruption, create five million jobs and pursue free market reforms
Would seek deeper relations with the Europe and the West
Ukraine's Central Electoral Commission chief Serhiy Kivalov urged all politicians "to calm down".
"The CEC will act strictly in conformity with the law," Mr Kivalov told reporters.
Kiev is on high alert, with extra police and soldiers on the streets.
The Central Election Commission is being guarded by at least four water cannon and two armoured personnel carriers.
During the campaign, Mr Yushchenko, prime minister between 1999 and 2001, claimed to have been the victim of intimidation and dirty tricks, including an alleged poisoning attempt.
His critics portray him as an American puppet who will do anything to gain power, including inciting civil unrest.
Turnout was at 79% despite plummeting temperatures, election officials said earlier.
Counting began immediately after the polls closed at 1800 GMT on Sunday.
However, the BBC's Helen Fawkes in Kiev says it could take some time for the final figures to be known.
After the first round on 31 October, it was 10 days before the overall result was released.
Then, Mr Yushchenko garnered 39.87% of the vote, compared to Mr Yanukovych's 39.32%.
International observers and the opposition said the first round was a step backwards for democracy in the former Soviet republic of 48 million people, alleging widespread fraud and intimidation.
The first results from the second round conflicted with two exit polls released immediately after voting ended.
The election was dogged by tension and abuse claims
The first exit poll, conducted by several Ukrainian research organisations, gave Mr Yuchshenko 54% of the vote, against Mr Yanukovych's 43%.
Another poll - by Ukraine's Social Monitoring Centre - put Mr Yushchenko ahead by 49.5% to 45.9%.
Mr Yushchenko's campaign chief, Oleksander Zinchenko, told the Kiev rally that the exit polls showed "a clear victory for our candidate", urging opposition backers to "defend this victory".
A huge screen was erected in the square to hold a parallel vote-count, which gave Mr Yushchenko a clear lead over his rival.
Mr Yanukovych's camp earlier described the figures of the two exit polls as ridiculous.
His campaign manager, Serhiy Tyhipko, said research by their own team showed the prime minister was in the lead by 3-5%.
Experts say some of the exit polls conducted after the first voting round had been inaccurate.
Both sides have complained of problems during Sunday's voting.
The authorities are investigating the killing of a policeman who was guarding ballot papers in a village in central Ukraine. The motive for the killing is not known.
And police said eight ballot boxes were set on fire in a western pro-Yushchenko part of Ukraine, AFP news agency reported.