The Supreme Council of the Armed Forces (SCAF) "invited all the political and national forces for an emergency dialogue to look into the reasons behind the aggravation of the current crisis and ways to resolve it as quickly as possible," it said in a statement carried by the MENA news agency.
The SCAF -- which took power when Hosni Mubarak was ousted by a popular uprising in February -- called on "all forces and citizens to commit to (restoring) calm, and creating an atmosphere of stability with the goal of pursuing the political process."
The statement came on the third straight day of clashes in Cairo's Tahrir Square that left 24 people dead, plunging Egypt into its worst crisis since Mubarak's fall.
The SCAF expressed its "deep sorrow over the deaths and injuries during the recent painful events, and offered its deepest condolences to the families of the victims."
It said it ordered security forces "to take all necessary measures to secure the demonstrators and to exercise the utmost restraint."