About 10 people were reportedly injured as police wielding batons forced opposition supporters away from the building, and an opposition leader, Levan Gachechiladze, was driven away in an ambulance.
The Georgian opposition is demanding, aside from President Mikheil Saakashvili's resignation, early elections in April 2008, electoral reform, and the freeing of "political prisoners".
At the peak of the protests, between 50,000 and 100,000 people, according to different estimates, rallied on Friday, the first day of Georgia's worst unrest since the 2003 "rose revolution" that brought Saakashvili to power.
The Imedi TV channel reported that a Georgian opposition leader detained earlier today has launched a hunger strike. Giorgy Khaindrava announced the measure after being transported to a Tbilisi court to face charges of inciting public disorder and resisting police. He was later released by the court after paying a fine of around $250.
National media also reported that authorities are searching the office of businessman Badri Patarkatsishvili, who earlier pledged to finance political opposition in the country.
Georgian lawmaker Levan Gachechiladze, who had been taking part in a hunger strike outside parliament, said he had been attacked by police, but warned that "the people will soon beat Saakashvili in the same manner".
Russian Foreign Minister Sergei Lavrov said the ongoing unrest is an internal affair for Georgia but stressed that Russia is concerned by the events. "What is happening in Georgia is its internal affair, and I would not like to comment in detail on the situation. But it is of concern to us," he said.
The minister said that in addition to the crisis in Tbilisi, Georgia's leadership is attempting to scupper talks on regulating the country's conflicts with its breakaway territories of Abkhazia and South Ossetia.
A spokesman for the European Council said the EU body is closely watching the situation in Georgia and urged the country's authorities and opposition to refrain from confrontation.