Koba Davitashvili, an opposition leader from the People's Party, said that protesters would not waver.
"There will be no dialogue with Saakashvili. Dialogue is possible on only one issue: his resignation," Davitashvili said.
Saakashvili has rejected the calls to resign and has offered to hold talks with the opposition.
"There is poverty in the country which has been aggravated by the war and the economic crisis and our citizens are angry today because of these problems. I am angry too," he said on Friday.
"It is not easy to overcome all of this ... It requires unity and dialogue."
Giorgi Kandelaki, a member of Georgia's parliament, told Al Jazeera that while Saakashvili would not step down, there was a need to address issues raised by the opposition.
"This protest once more shows that the government should redouble its effort to broaden political dialogue, which is ongoing with the opposition," he said.
Protests began on Thursday, when tens of thousand of people gathered outside parliament, waving flags and chanting "resign".
Opposition leaders are angry at Saakashvili's handling of last year's Russia-Georgia war and accuse him of failing to deliver promised democratic reforms.
Critics have also accused him of betraying the principles of the 2003 Rose Revolution, in which he came to power.
Matthew Collin, Al Jazeera's correspondent in Tbilisi, said the protesters marched on Saakashvili's official residence on Saturday as well as a television station that they accuse of broadcasting pro-government propaganda.
But the government has ordered police not to arrest or touch the protesters unless the crowds try to storm government buildings, because Georgia wants "to be seen as a European-style democracy", Collin said.
In November 2007, riot police used rubber bullets, tear gas and water cannon to disperse thousands of anti-government protesters, a move that prompted condemnation of Saakashvili.