Opposition leaders said they had rejected violence and would apply psychological pressure on the authorities.
"We do not want a violent regime change," said Georgia's ex-state minister, Giorgy Khaindrava. "We will pursue this goal by peaceful, civilized and constitutional means - through elections."
Protesters formed a human ring around the parliament building, shouting out resignation demands for Mikheil Saakashvili.
Several members of the opposition bloc have announced open-ended hunger strikes.
"I am announcing a hunger strike, which will continue until all our demands are met. I will not leave this place until the demands are satisfied," Levan Gachechiladze, an opposition lawmaker, said sitting on the steps to the parliament.
Earlier on Monday, opposition activists formed what they called a "corridor of shame" in front of the Interior Ministry inviting civil servants, who could not avoid to pass through it, to quit their jobs and join the rallies.
The opposition in the Caucasus state initially demanded Saakashvili annul his decision to move parliamentary elections back to fall 2008, urged democratic changes to electoral procedures, and the release of political prisoners, whose existence the authorities have denied. But protesters later focused on demands for the president's resignation.
Republican Party leader David Usupashvili said on Monday the opposition would now seek dialogue with Parliamentary Speaker Nino Burdzhanadze, who has held two meetings with opposition leaders since street protests began on Friday.
Speaking after talks on Monday, Burdzhanadze said: "... my meeting with the opposition factions' leaders was very helpful. I hope dialogue will continue and constructive results appear."
On Sunday, in his first public appearance since Friday, Saakashvili rejected the opposition demands, reaffirmed his plans to run for a second presidential term next fall and accused Russia of orchestrating unrests in Georgia.
The ex-Soviet state is witnessing its worst crisis since the 2003 "rose revolution" which brought Saakashvili to power.
U.S.-educated Saakashvili has sought closer ties with Washington, Europe and NATO membership for Georgia. He has also vowed to regain control of two breakaway regions and decrease Russia's influence on the country. But his opponents accuse him of growing increasingly authoritarian.
