The Muslim Brotherhood has held talks with Vice President Omar Suleiman to press 'legitimate and just demands' as the government attempts to end 12 days of protests.
Senior Brotherhood leader Mohammed Mursi said the group was sticking to the protesters' main condition that President Mubarak stand down.
They are the first known discussions between the government and the Brotherhood in years, suggesting the group could be allowed an open political role in the post-Mubarak era.
Some opposition leaders met with Mr Suleiman over the weekend, but said they had been no breakthrough.
Defiant: A protester has a precarious nap on the track wheels of a tank near Tahrir Square, Cairo
Staying put: Hundreds of Egyptians pray in Tahrir Square after nearly two weeks of protests. Anti-government supporters insist that President Mubarak steps down
Mr ElBaradei said there was still a 'hard core' who would not give up protesting as long as Mr Mubarak held on to power.
Talks: Opposition group the Muslim Brotherhood will hold discussions with the Egyptian government today for the first time in years
Daily life: Banks and shops reopened their doors today after nearly two weeks of protests across Egypt
Protesters flee from tear gas fire during clashes in Cairo January 28, 2011. REUTERS
Anti-government protesters take part in Friday prayers at Tahrir Square in Cairo February 4, 2011. REUTERS
A woman opposition supporter takes shelter while providing water during rioting with pro-Mubarak demonstrators near Tahrir Square in Cairo February 3, 2011.
Opposition supporters throw stones at pro-Mubarak demonstrators in Tahrir Square in Cairo February 3, 2011. REUTERS