The numbers of demonstrators has gradually dropped away since the first day, with 25,000 turning up on Friday, and around 4,000 gathering over the weekend.
But opposition leaders are hoping to widen their "civil disobedience" campaign by clogging the city's roads and expanding protests across the country.
Saakashvili has vowed to serve out his second term, which ends in 2013, and has urged opposition leaders to enter talks with the government.
Matthew Collin, Al Jazeera's correspondent in the capital, said the protesters had marched on Saakashvili's official residence on Saturday as well as a television station that they accuse of broadcasting pro-government propaganda.
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.
Opposition leaders are unhappy with Saakashvili following last year's conflict with Russia, in which Georgia lost territory as separatists and their Russian allies took full control of two breakaway Georgian regions.
Critics have also accused him of betraying the democratic reforms promised during the 2003 Rose Revolution, in which the president came to power.
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's actions.