Crowds of protesters, who have occupied the city's Tahrir Square for two weeks, say they will only leave when President Hosni Mubarak stands down.
The government offered a series of concessions at Sunday's talks, but the opposition said they were not enough.
US President Obama has said Egypt will not "go back to what it was".
Opposition groups met members of the government on Sunday to discuss how to resolve the stand-off which has paralysed the country and left some 300 people dead.
Vice-President Omar Suleiman hosted the talks. Six groups were represented, including a coalition of youth organisations, a group of "wise men" and the banned Muslim Brotherhood in its first ever meeting with the government.
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