Protesters have given Mr Saakashvili 24 hours to respond to demands
Organisers of a mass rally against Georgian President Mikhail Saakashvili have called on him to resign or face a new day of protests in Tbilisi.
His main error, opposition parties say, was to lead the country into war with Russia last year and plunge the country into what they call a crisis.
But he hit back on Friday, vowing to stay in office until his term ends in 2013, Itar-Tass news agency reported.
Up to 60,000 people attended Thursday's opposition rally in the capital.
Hundreds remained in the city centre overnight.
They have given him until 1100 GMT on Friday to agree to their demand.
"This is the last chance for the authorities to stand above personal interests and to act responsibly to overcome the most difficult crisis in the country," the organisers said in a joint message.
Opposition leader Levan Gachechiladze said they had "no other choice but to stay here until our demand is met".
Mr Saakashvili appealed for "dialogue and sharing responsibility" on Friday, Reuters news agency reported. He urged "unity across the political spectrum".
The leaders of the opposition parties did not make clear what the consequences would be of him failing to resign, but both sides have insisted that they will not resort to violence, the BBC's Tom Esslemont reports from Tbilisi.
President Saakashvili refused to resign on Thursday, urging Georgians to show unity and "work day and night... to finally liberate Georgia".
He was speaking at a ceremony in Tbilisi to commemorate the day, 20 years ago, when 20 people died as Soviet Red Army troops crushed a protest in the same place.
"It is absolutely clear that no matter what opinions we may hold and how we may differ from each other, we have one homeland," he said.
He linked the events of 1989 to those of last August, when Georgia was defeated in a brief war against Russia over its breakaway province of South Ossetia.
"This is what these people sacrificed themselves for under Russian tank tracks, and what our fighters sacrificed themselves for last August... freedom and a united Georgia," he said.
Opposition leaders have appealed to the government not to use violence to break up mass protests.
Police used rubber bullets and tear gas to break up the last mass protests in Tbilisi in November 2007.
Our correspondent says this is the most organised protest since the war with Russia and it is one that opposition leaders are likely to be pleased with.
Estimates of the crowd ranged between 50,000 and 60,000, news agencies reported. Organisers had expected up to 100,000.
The opposition alleged that dozens of members were arrested before the rally - a claim denied by the government.
"The Georgian police has not arrested a single protester and has not blocked a single road," said Ms Zguladze.
Our correspondent says both opposition and government figures had accused one another of planning to use violence at the rally.
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