"We are giving Saakashvili two or three days to sit down at the negotiating table," said National Forum party leader Irakly Melashvili.
Otherwise, he warned, their plan to block the country's highways would go ahead.
Other opposition leaders said earlier in the day they were ready to meet with Georgian authorities to discuss ways of bringing an end to the current violence.
The opposition, who have been demonstrating against the president on the streets of the capital for the past month, claim over 60 people, including six police officers, were injured in clashes at a police compound in the Tbilisi suburb of Didi Digomi, on Wednesday night. 29 people were hospitalized.
"We are ready to meet [with the authorities] to consider ways of overcoming the severe political crisis that has affected the country," said Irakly Alasania, former Georgian ambassador to NATO and now leader of the opposition Alliance for Georgia.
Salome Zurabishvili, the leader of the Georgian Path party, said "it is necessary for Saakashvili to wake up, face up to reality, meet with us and offer his vision of ways of dealing with the situation."
She said, however, that the opposition would not abandon its demand that Saakashvili step down and would continue pushing for his resignation by peaceful means.
"Saakashvili wants to plunge the country into an abyss. But we don't want this to happen. This is why there will be a powerful wave of protests on May 9. We have no way to retreat - not a step back," she said.
The country's patriarchate has described the situation in Tbilisi as highly charged and urged everybody to remain calm, also calling for the authorities to introduce measures as soon as possible to ease tensions.
