The announcement was made today by United Front leader and former Prime Minister Feliks Kulov.
"We're sticking to our previous positions -- an early presidential election and carrying out the constitutional reform," Kulov said. "At the same time, I have to say that today a majority of members from the United Front -- regular members, I have to underline -- put before us a new demand. This is the resignation of the president."
Speaking at a press conference in Bishkek, Kulov also said he was ready to meet with Bakiev -- but only in public.
Presidential press secretary Nurlan Shakiev told RFE/RL that Bakiev is prepared for talks with the opposition, but said the opposition should not try to impose its conditions.
Meanwhile, more than 60 opposition activists started a hunger strike in traditional nomadic tents (yurts) in front of parliament.
And dozens of Bakiev supporters are holding rallies in both the capital and the southern town of Jalal-Abad, calling on the opposition and the government to settle their dispute by dialogue.
Today's developments come as new Prime Minister Almaz Atambaev almost completed the formation of his coalition government.
(with material from 24.kg, AKIpress, ITAR-TASS, Interfax)