Secular and leftist groups have also called for mass demonstrations and public prayers across Egypt to support what they see as a popular revolution that led to the overthrow of Morsi by the military on July 3 after just a year in office.

In one apparent conciliatory gesture, prosecutors dropped the main charge against the head of the Brotherhood's political wing, Saad El-Katatni, on Wednesday in a possible prelude to releasing him.

The person involved in the mediation effort said a sequence of statements and confidence building measures aimed at reducing tensions and reassuring public opinion might yet lead to direct or indirect negotiations between the two sides.

So far, the Brotherhood has refused to accept what it calls an illegal coup against Morsi and has publicly demanded the return of the elected president, who is detained at a secret location.

The new authorities have accused Islamist leaders of inciting violence, frozen the Brotherhood's assets and vowed to put them on trial.

Train has departed

"The train of the future has departed, and everyone must realize the moment and catch up with it, and whoever fails to realize this moment must take responsibility for their decision," interim president Mansour said in an Eid broadcast.

Diplomats have said any settlement would have to involve a dignified exit for Morsi, Brotherhood acceptance of the new disposition, the release of political prisoners arrested since the takeover and a future political role for the Brotherhood.

The United States and the EU said on Wednesday they were very concerned that the Egyptian parties had not found a way to break what they called a dangerous stalemate.