The initiative led by Egypt's Gamaa Islamiya and Islamic Jihad movements, which waged an insurgency in the 1990s, aims to start talks between the military and the Muslim Brotherhood, from which President Mohammed Mursi was overthrown by the military on July 3 after millions took to the street demanding that he step down.
Mr Mursi's allies had previously insisted he be restored to power as a starting point for any talks but Islamic Jihad leader Mohammed Abu Samra said negotiations had no "red lines".
The groups do not speak for the Brotherhood but the initiative is a new sign of flexibility from the pro-Mursi alliance of mostly Islamist groups and comes as the Islamists' protest campaign wanes and numbers at their formerly massive rallies dwindle.
Hundreds of Brotherhood leaders and organisers have been arrested in the crackdown. Egypt's worst bout of violence in its two years of turmoil was set off when security forces moved in to break up two sprawling pro-Mursi protest camps on August 14.