Crowds of protesters, who have occupied the city's Tahrir Square for two weeks, say they will leave only 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.
Egyptian state TV said the participants had agreed to form a joint committee of judicial and political figures tasked with suggesting constitutional amendments.
But opposition leaders said they were sceptical of the government's motives and that the measures did not go far enough.
The Muslim Brotherhood said it would take part in future talks only if the government made progress on meeting its demands that Mr Mubarak resign, parliament be dissolved, emergency laws be lifted and all political prisoners released.
Senior Brotherhood figure Essam el-Erian told reporters the authorities had responded to some of the demands but only in "a superficial way".
Meanwhile, one Egyptian security officer was injured when four rocket-propelled grenades were fired at a security forces barracks in Rafah on the Gaza Strip border, officials said. It was not immediately clear who was behind Monday morning's attack.
Debt issues Many Egyptians have been wondering how quickly daily life will return to normal, regardless of the outcome of the struggle for power.
The authorities have been attempting to restore a sense of normality to the capital, where banks opened for the first time in a week on Sunday, drawing long queues as people waited to withdraw money.
The traffic police are back at work in the capital. Schools remain closed, however, and resumption of business at the stock exchange has been postponed for 24 hours, as the government attempts to sell $2.5bn (ÂŁ1.55bn) in short-term debt. The government is seeking to revive an economy said to be losing at least $310m a day.
The protesters are still occupying central Tahrir Square, where some slept overnight inside or beneath the tracks of the army vehicles there, to stop any move to corral the demonstration into a smaller area.
On the talks front, leading opposition figure Mohamed ElBaradei - who was not at the talks but sent a representative to meet Vice-President Suleiman separately - described the process as "opaque".
He said he was proposing a one-year transitional period where Egypt would be run by a three-member presidential council as it prepared for elections.
'Grapple with reality' President Mubarak has so far refused to resign, saying that to do so would cause chaos. He has instead said he will not stand for re-election in September.
But US President Barack Obama has insisted that an "orderly transition" must begin immediately.
In an interview with Fox News on Sunday, he said: "The Egyptian people want freedom, they want free and fair elections, they want a representative government, and so what we've said is, you have to start a transition now."
http://www.bbc.co.uk/news/world-middle-east-12378828