Protesters displayed an effigy of President Mikheil Saakashvili sporting a Hitler-style moustache and said they would continue rallies until their demands are met.
The protesters are also demanding changes to electoral procedures, and that parliamentary elections be moved forward to April 2008.
"We don't plan to leave," Zviad Dzidziguri, a member of the Conservative Party said. "Let us see whose nerves are stronger. We will stand until the end, even at the cost of our lives."
Some 200 people are ready to join an opposition hunger strike now underway outside the parliament, Giorgy Khaindrava, an ex-Cabinet minister and an opposition leader, said on Tuesday. He said 300 people had already joined the hunger strike, and that that their total number is expected to reach 500.
Between 50,000 and 100,000 people, according to different estimates, rallied on Friday, the first day of Georgia's worst unrest since the 2003 "rose revolution" that brought Saakashvili to power.
Saakashvili is accused by opponents of corruption, totalitarian tendencies, and of overseeing failed economic reforms.
The president has flatly rejected the opposition's demands, and accused Russia of orchestrating the unrest in the ex-Soviet Caucasus state.
Russia's foreign minister, Sergei Lavrov, dismissed the charges as absurd on Tuesday. "I would not like to comment on the actions of this political figure. The farce that accompanied the Georgian leadership's actions is obvious to all."
The comments triggered an angry reaction from the Georgian government and opposition alike. The Russian ambassador to Georgia was summoned to the Foreign Ministry to give an explanation.
Zviad Dzidziguri said: "Lavrov should take care of Russian affairs and let Georgia tackle its problems on its own."
About 20 young opposition activists organized a picket in front of the Russian Embassy in Tbilisi, shouting "Moscow, take Saakashvili back to Russia!"
The U.S. ambassador in Tbilisi, John Tefft, said on Tuesday that the United States will do all it can to help Georgia overcome its political crisis.
President Saakashvili, who has pushed for NATO membership for Georgia, until recently enjoyed Western backing in his ongoing disputes with Russia, in particular over two breakaway regions that have strong ties with Moscow.