A snap presidential election in the ex-Soviet republic of Georgia was democratic and the outcome should be respected, foreign observers say.
Thousands of opposition protesters disputed the result
OSCE and Council of Europe officials said the poll had been consistent with international democratic standards - though they did refer to some problems.
Early results suggest President Mikhail Saakashvili won, but it is unclear if he did well enough to avoid a run-off.
But opposition groups allege the vote was rigged and have staged protests.
"We are not going to let him [President Saakashvili] steal the election," one opposition leader told the BBC.
An estimated 5,000 or more people gathered in the snow in a square in the capital, Tbilisi, on Sunday - the Orthodox Christmas Eve.
Opposition leader Levan Gachechiladze - the most prominent of the five other presidential candidates - told the crowd: "We will defend our vote by legal means."
He said exit polls had been "falsified".
The polls suggested President Saakashvili won more than 53% of the vote and Mr Gachechiladze 28%.
Officials said that with 7% of the votes counted, Mr Saakashvili had at least 55% of the ballots.
Official results are expected later on Sunday.
If Mr Saakashvili wins more than half of the vote, he will be elected without the need for a second round. But several opposition parties will be hoping that he falls short, and that they can unite behind Mr Gachechiladze in a run-off.
The opposition parties say that they want to do away with the office of president, and that if Mr Gachechiladze wins he will step down in favour of a parliamentary system.
The head of the observer mission, US Congressman Alcee Hastings of the Organisation for Security and Co-operation in Europe (OSCE), said: "I perceive this election as a valid expression of the choice of the Georgian people."
He said there had been some shortcomings - notably that Mr Saakashvili's campaign had overlapped with state activities, and this "contributed to an inequitable campaign environment".
But he praised the "calm and peaceful atmosphere" during the election, in which he said "democracy took a triumphant step".
Matyas Eorsi, the head of a monitoring group from the Council of Europe, also endorsed the election, adding: "I would like to make a plea to all political actors to respect the legitimacy of the election for the stability of Georgia."
The United States urged the opposition to respect the monitors' verdict.
Russia, however, called that verdict "hasty" and "superficial".
Close to West
Mr Saakashvili's supporters began celebrating - some waving flags and blaring car horns - as soon as exit polls suggested he had won.
Mikhail Saakashvili has steered Georgia away from Russia
But he acknowledged the exit poll results were not yet confirmed.
Mr Saakashvili called the early election in an attempt to prove his democratic credentials after huge opposition protests were suppressed in November.
Georgians were also asked to vote on whether they should have a parliamentary election in the coming months, and whether the country should join Nato.
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.