According to the Novosti Georgia news agency, Burdzhanadze reported this to a news conference following a meeting with Georgian President Mikheil Saakashvili Wednesday.
"I talked with Adzharian leader Aslan Abashidze on the phone at daybreak, at about 4 o'clock in the morning , and advised him that he should voluntarily step down," Burdzhanadze told the media.
"I believe this to be the only way out for Adzharia's incumbent leadership and its entourage," she added.
The Parliament Speaker believes that the Adzharian leader should follow in the wake of Eduard Shevardnadze, who resigned as President of Georgia in November 2003.
"I think the events that occurred in Georgia just five or six months ago, when the leadership failed to heed to the people, should serve as a vivid example for the Adzharian leadership. The population wants today's Adzharia to develop in different conditions. I recommend to Abashidze and urge him to voluntarily step down," Ms. Burdzhanadze said.