Ms Suu Kyi spoke to thousands of supporters outside her opposition party headquarters yesterday, a day after her party claimed she had won a parliamentary seat in closely watched by-elections.
The 66-year-old democracy champion called the election "a triumph of the people", and said: "We hope this will be the beginning of a new era."
Official results have not yet been released.
If confirmed, the victory would mark a major milestone in the south-east Asian nation as it emerges from an era of military rule – as well as an astonishing reversal of fortune for a woman who became one of the world's most prominent prisoners of conscience.
"The success we are having is the success of the people," Ms Suu Kyi said, as a sea of supporters chanted her name and thrust their hands into the air to flash "V" for victory signs.
"It is not so much our triumph as a triumph of the people who have decided that they have to be involved in the political process in this country," she said. "We hope this will be the beginning of a new era."
If confirmed, Ms Suu Kyi will take public office for the first time and lead a small bloc of opposition lawmakers in Burma's military-dominated Parliament."