"Today we have realised that if we ourselves do not take back control of our country, do not return our statehood, then we will have to face this problem for many years to come."
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."
Koba Davitashvili, an opposition leader from the People's Party, said on Saturday that protesters would not waver in their calls for the president to leave office.
"There will be no dialogue with Saakashvili. Dialogue is possible on only one issue: his resignation."
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," Kandelaki said.
Protests began on Thursday, when at least 60,000 people gathered outside parliament, waving flags and chanting "resign".
Opposition leaders, angry at Saakashvili's handling of last year's Russia-Georgia war and accusing him of failing to deliver promised democratic reforms, have said they will carry on protesting until he resigns.
David Gamkrelidze, leader of the New Rights party, said: "If [Saakashvili] does not accept our demands, we will intensify pressure and the protests will be sharper, not only outside parliament but in other places as well, for example outside the presidency."
Tired of protests
Matthew Collin, Al Jazeera's correspondent in Tbilisi, said despite the protests, there were signs that Saakashvili still had an element of popularity.
"A lot of Georgians simply want stability," he said.
"They are tired of endless protests in the street, they want to get on with their lives and they want the economy to develop, and they feel political unrest won't allow that to happen."
Opposition to Saakashvili has been growing since the Russia-Georgia war, in which Georgia was defeated.
The conflict has emboldened opponents who argue that Saakashvili has made too many mistakes to remain in power until 2013.
Critics have also accused him of betraying the democratic reforms promised in the 2003 Rose Revolution, in which he came to power.