The largely peaceful demonstration against the president has brought at least 100,000 people out on to the streets of the capital.
"Society demands that Mikheil Saakashvili acts correctly and fulfills the will of the people," an opposition statement said. "This is the last chance for the leadership to rise above their personal interests and for the state to show responsibility in its approach to the task of getting the country out of this complex crisis."
The Georgian leader's popularity has plummeted since last August's disastrous war with Russia, and his failure to carry out the democratic reforms promised after the 2003 "Rose Revolution" that brought him to power.
"Saakashvili has to give the nation a chance to peacefully change power by constitutional means... to show the entire world that we are a worthy and civilized nation," the opposition said.
The opposition said they would inform the nation of Saakashvili's response to their demands in 24 hours and draw up a corresponding plan of action.
Hundreds of riot police have been deployed in front of the parliament building and the presidential administration. Fire crews are also at the ready, in apparent anticipation of arson attacks similar to those seen during this week's anti-government riots in Moldova.
The opposition Democratic Movement-United Georgia party, led by Saakashvili's former ally Nino Burjanadze, earlier said that 60 of its activists had been arrested during the night. The Interior Ministry denied the report.
"Our sole demand and goal is Saakashvili's resignation," Burjanadze said outside parliament on Thursday. "We must achieve this through peaceful means."
Anti-Saakashvili protests in November 2007 were broken up by riot police using rubber bullets, tear gas and water cannons. U.S.-based rights group Human Rights Watch said over 500 people were injured in the crackdown.
