Protesters in the Geogrian capital, Tbilisi, have been on the streets since April 9 demanding the president's resignation.
"Saakashvili's regime has several days left. They will not be able to withstand the pressure from the people any longer," said Salome Zurabishvili, who heads the Georgia's Way opposition party.
The opposition leader said in her speech that "the nerves of Saakashvili and [Interior Minister Vano] Merabishvili were severely frayed" by the ongoing protests.
"We will not take a single step backwards," Zurabishvili added.
Saakashvili, a U.S.-educated lawyer who came to power on the back of 2003 street protests, has been criticized for his authoritarian leadership and for dragging the country into a disastrous war with Russia last August, which resulted in the permanent loss of two separatist provinces.
The opposition has built wooden jail cells on Tbilisi's central street to symbolize the country's descent into a police state, and thousands of new supporters arrived in the capital from provinces late on Wednesday. Police have not attempted to disperse the rallies.
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The main event of the third day of the 11th meeting of the Valdai International Discussion Club in Sochi was the closing session with President Vladimir Putin. The atmosphere was calm and open, despite the current political tensions and the Russia-West confrontation. The Russian president said that it corresponded to the spirit of the Valdai Club.