Up to 20,000 protesters responded to opposition calls on Friday to take the dispute over a 2 November election result to the streets.
The protesters appeared determined but peaceful, hundreds dancing to an impromptu folk concert outside parliament square.
Opposition leader Mikhail Saakashvili, stepping up the pressure on the president, demanded "total civil disobedience".
He said: "This man stole everything from us and he is not going to take notice of his own people... Never in Georgia were the people so mobilised against the government."
Saakashvili called on the army to disobey the president's orders, urged state workers to strike and police not to go to work.
He also called on all Georgians to take to the streets day after day until the president steps down.
As evening fell, thousands formed a human chain around the presidential office building, a yellowish Soviet monolith.
Shevardnadze says he will not
step down under street pressure
Interior Ministry troops watched as protesters chanted "step down" and "traitor".
Earlier, correspondents saw armoured vehicles, trucks and buses with soldiers in body armour outside the Interior Ministry. The ministry has said it will use force only if protesters target government buildings.
The protests, the largest in Georgia since the end of a bitter civil war in the early 1990s, were watched anxiously by Western governments and oil firms hoping for a return to stability.
The turmoil has threatened to plunge Georgia into chaos and dash Western hopes of a stable partner in the region to ensure construction of an oil pipeline to cut out Gulf ports.
The United States on Friday renewed calls for the Georgian government and opposition to avoid bloodshed.
"We believe that it is important for all sides to respect the role of peaceful assembly in the political process and to take all steps to prevent violence," deputy State Department spokesman Adam Ereli said.
"We are urging the speedy resolution of the election situation and the announcement of a final vote count. This is something that the Georgian people and political parties are going to have to resolve."
"We believe that it is important for all sides to respect the role of peaceful assembly in the political process and to take all steps to prevent violence"
He added: "We hope that they do it peacefully through dialogue in a way that respects the rule of law and meets the needs of the people and institutions of Georgia."
The crisis was triggered by a disputed parliamentary election almost two weeks ago, in which the opposition said it was robbed of victory.
Attempts at talks were launched on Sunday, but ended on Wednesday when Saakashvili walked out.
Shevardnadze was hailed as the saviour of Georgia when he became head of state in 1992.
But his popularity has waned and he is now despised for failing to raise living standards, root out corruption and reunite the country.
He warned earlier that the confrontation was coming dangerously close to civil war and said it would be "irresponsible" for him to resign under street pressure.