Tahrir Square in central Cairo was quieter early Wednesday than earlier in the week - even as opposition groups rejected outright President Hosny Mubarak's pledge to step down at the end of his term in September, DPA reported.
Protesters, who had staged the largest demonstrations Egypt had seen in generation, were demanding the immediate ouster of the president, who has ruled for 30 years.
Mubarak said on Tuesday evening that he wanted to use the remaining seven months in office for a "peaceful handover" of power. The question being raised in Cairo was if the compromise offered would satisfy citizens.
Mohammed Mursi, a spokesman for the Muslim Brotherhood, said, "This satisfies none of the people's demands," adding that 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 also dismissed by the April 6 Youth Movement.
"We reject that because it does not fulfill 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.
After Mubarak addressed his nation in a televised address, US President Barack Obama said Egypt's transition to democracy and toward free and fair elections "must begin now" and should allow all opposition figures to participate.
"What is clear, and what I indicated tonight to President Mubarak is my belief that an orderly transition must be meaningful, it must be peaceful, and it must begin now," Obama said.
US media reported that the president might have preferred a faster move to a transitional leadership in Egypt, a key ally which receives 1.5 billion dollars in aid annually, mostly to the military.
It was unclear if the US, which has entered into a dialogue with ElBaradei, would also be willing to speak with the Islamist Muslim Brotherhood, still the country's largest organised opposition force.
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, and state television announced larger pro-government rallies were planned for Wednesday.