They also accuse him of becoming increasingly autocratic since he came to power after the peaceful 2003 Rose Revolution.
Burjanadze said: "Today, the Georgian people have shown to the world and to themselves that they're ready to struggle to the very end.
"You have frightened those who want to frighten you."
The crowd sang the national anthem in the stadium and observed a minute of silence for those who died during the war.
"Saakashvili must leave because he ceded our territories to the Russians," Natela Urashvili, a 49-year-old dentist, said.
The demonstrators later marched to the city's main cathedral, where opposition leaders held talks with the head of the country's Orthodox Church on how to proceed in the political standoff.
The Georgian opposition has been staging daily protests since April 9 in the biggest demonstrations against Saakashvili's rule since the conflict with Russia.
The Georgian leader has rejected resignation calls and offered to hold talks on democratic reforms.
The May 26 comemmoration, one of two main patriotic holidays in Georgia, marks the date that the country declared independence from Russia in 1918 and started a short-lived republic.