Led by a popular Muslim television evangelist, Sheikh Metwalli al-Sharaawi, the 25-strong group met the Interior Minister, Mohammed Abdel-Halim Moussa, last week after receiving word from militants that they were ready to talk, said Fehmi Huweidi, a writer on Islamic affairs who joined the team.
It was the latest attempt to seek a political solution to the crisis since the unrest, which has killed more than 120 people, flared last year.
The group, which is not affiliated to any organisation, raised the possibility of allowing Islamic political parties and the freeing of militants detained without trial, Mr Huweidi said. Team members will visit militant leaders in Egyptian prisons during the next few weeks.
Islamic leaders and intellectuals known as sympathetic to 'the Islamic wave' had been thinking of an initiative for about three months, Mr Huweidi said. They were encouraged about two weeks ago when lawyers defending militants on trial relayed a message that the extremists were ready to talk.
Publicly, the government has said it cannot talk to extremists who have harmed Egypt's vital tourist industry with attacks on foreigners in a drive to establish a purist Islamic state. The authorities have launched an increasingly bloody series of raids to crush the miltants, killing 29 of them last month alone.
Government officials privately met militants in the Islamic stronghold of Assiut last summer.