The opposition Muslim Brotherhood has criticized Egyptian President Hosny Mubarak's offer not to run again for the post when his term is up.
Mubarak said on Tuesday evening that he wanted to use the remaining months of his period in office for a "peaceful handover" of power, DPA reported.
Mohammed Mursi, a spokesman for the Muslim Brotherhood, said, "This satisfies none of the people's demands."
Mursi said the concession came too late.
Nobel Peace Prize laureate Mohammed ElBaradei, who has emerged as an opposition figure, said, "As always he is not listening to his people."
The 82-year-old president's offer not to run for office again in September was dismissed by the April 6 Youth Movement.
"We reject that because it does not fulfil our demands," a spokesman for the group said in Cairo.
"We will continue the protests until our demands are met, especially the call for the resignation of Mubarak and his government.
Anti-government demonstrators took part in the largest rally yet on Tuesday, the eighth consecutive day of protests, with over a million people across the country taking to the streets
Around 2,000 supporters of Mubarak also demonstrated Tuesday, witnesses said.