"It is not easy to overcome all of this... It requires unity and dialogue."
Matthew Collin, Al Jazeera's correspondent in Tbilisi, said groups of a few thousand protesters had split off from the main rally, marching towards Saakashvili's official residence and the state broadcaster.
"They're trying to raise the stakes in this political dispute, they're trying to raise the pressure on president Saakashvili," he said.
Giorgi Kandelaki, a member of Georgia's parliament, told Al Jazeera that while the president 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 at least 60,000 people gathered outside parliament, waving flags and chanting "resign".
Opposition leaders, angry at Saakashvili's handling of the Russia-Georgia war and accusing him of failing to deliver promised democratic reforms, have said they will carry on protesting until he resigns.
Several hundred protesters camped overnight outside Georgia's parliament building, and continued to block the streets there on Friday.
David Gamkrelidze, leader of the opposition 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."
|Mikheil Saakashvili has said he will not step down, despite the protests [AFP]
Matthew Collin 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're 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 the president has been growing since last year's Russia-Georgia war, in which Georgia was defeated.
The conflict has emboldened opponents who argue the president has made too many mistakes to remain in power until 2013.
Critics have also accused the president of betraying the democratic reforms promised in the 2003 "rose revolution", in which he came to power.