Georgian President Mikhail Saakashvili has a commanding lead in the country's snap election but it is unclear whether he has avoided a presidential run-off.
Exit polls suggest he won 53.7% of the vote, which if confirmed by official results would give him an outright win.
But analysts are urging caution as 20% of respondents in the exit poll refused to say who they had voted for.
The vote is seen as a democratic test for the ex-USSR state after recent opposition protests were suppressed.
However opposition candidate Levan Gachechiladze has accused the government of trying to rig the election.
The exit polls, which suggest Mr Gachechiladze won 28% of the vote, were denounced as a "big lie" by an opposition spokesman.
The authorities have denied allegations of fraud, and acting President Nino Burjanadze told the BBC that the elections had been "free, fair and democratic".
But the BBC's Matthew Collin in Tbilisi says that after a bitter and divisive election the dispute seems certain to continue.
Mr Saakashvili called the election after huge opposition protests were suppressed in November, in an attempt to prove his democratic credentials.
Along with the presidential election, Georgians are being asked to vote on whether they should have a parliamentary election in the coming months, and whether the country should join Nato.
Hundreds of foreign observers have been monitoring the ballot.
Mr Saakashvili, a US-educated lawyer, came to power after street protests in 2003, dubbed the Rose Revolution.
His term as president has seen Georgia strengthen its ties with Nato and the European Union.
But relations with Moscow have soured and Georgia's economy has been badly hit by a Russian ban on Georgian goods.