Mr Shevardnadze will prosecute anyone who tries to use force
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Opposition groups in Georgia are urging supporters to continue mass protests to demand the president's resignation.
They say Sunday's parliamentary elections have been rigged in favour of Eduard Shevardnadze's For a New Georgia bloc.
Two days of fresh protests are planned, with demonstrations in provincial towns on Friday followed by a larger rally in the capital, Tbilisi, on Saturday.
There is still no official result from the ballot which observers say suffered spectacular irregularities.
Latest results show that a regional party which supports Mr Shevardnadze has made a very strong showing, lying in second place behind his bloc.
Prosecution threat
The results for the Revival Party, run by Ajaria regional leader Aslan Abashidze, contrast with exit polls.
The main opposition bloc, the National Movement, says the result is further evidence of vote rigging, and accuses the president and leaders of the regional opposition party of conspiracy to deprive them of their majority in the parliament.
Mr Shevardnadze has warned he will prosecute anyone who tries to use force to settle the dispute.
His warnings have been backed by the deployment of riot police in the capital.
But National Movement leader Mikhail Saakashvili called on Georgian society to "close ranks" in peaceful protest and force the government to stop rigging the results.
He told Georgian television: "Georgian society demonstrated an amazing courage and inflicted a catastrophic defeat on the current government of Georgia.
"We are facing an attempt to trample down the will of the people and to misappropriate power.
"It is essential that Georgian society closes ranks and, by peaceful means, averts a coup d'etat and the misappropriation of power by Shevardnadze and Abashidze."
He said peaceful actions would be held in Zugdidi, Gori, Zastaponi, Telavi and some other towns on Friday. On Saturday, he said, "the whole of Georgia will move towards Tbilisi and a large peaceful action will be held in the Tavisuplebis Moedani (the main square)".
The BBC's Chloe Arnold in Tbilisi said pre-election polls had shown much of the population intended to vote for the opposition, blaming Mr Shevardnadze for a sharp decrease in living standards since the collapse of the Soviet Union.
Following the election, international observers delivered a damning assessment of the process, saying they had witnessed spectacular irregularities.