The campaign officially began at 6:00 p.m. local time (14:00 GMT), with protesters crowding outside parliament and the presidential offices, and blocking the route to the state broadcaster. Opposition leaders have pledged to keep the protests peaceful, but to continue until Saakashvili steps down.
Saakashvili is currently facing the toughest challenge yet to his leadership, with 60,0000 people rallying against him in the capital on Thursday, amid public anger over last summer's disastrous war with Russia and Saakashvili's authoritarian leadership.
Addressing the crowd outside parliament during the afternoon, opposition leader Levan Gachechiladze, a former presidential challenger, urged Tbilisi residents "to demonstrate exemplary disobedience... This will start in Tbilisi and will then sweep across Georgia. I am, therefore, asking you to show discipline, as you did yesterday."
President Saakashvili remained defiant however, saying he would remain in office until his presidential term expires in 2013.
Speaking to reporters in English, he said: "I've been facing these ultimatums every other month during the last five years... Every independent poll clearly proves that people are longing for dialogue, for long-term stability."
However, he said he was ready to negotiate on several issues, including electoral reform.
Addressing the rally outside parliament, Nino Burdzhanadze, leader of the United Georgia Democratic Movement, challenged Saakashvili to a public debate on television.
"I'm calling on Saakashvili to engage in direct dialogue. If Saakashvili is a real man, I'm ready to join him in a live TV debate today and raise my complaints," she said.
Hundreds of protesters stayed in front of parliament overnight, and around 25,000 joined them during the day.
Saakashvili's opponents blame him for dragging the country into a war with Russia over South Ossetia last August, resulting in the permanent split from Georgia of the province, along with another rebel republic, Abkhazia. He also faces criticism for failure to carry out democratic reforms promised after the 2003 "Rose Revolution" that brought him to power.