The interim government led by Essam Sharaf resigned last week as protests against army rule intensified in Cairo and other cities.
The violence has left at least 40 people dead, including a 21-year-old activist who was "mistakenly" hit by a police convoy fleeing from a group of attackers near Tahrir Square on November 26.
Protesters have rejected concessions by the military rulers, including the naming of a 78-year-old veteran of Egyptian politics, Kamal Ganzouri, to lead a new government.
State TV reported Ganzouri has offered Cabinet positions and is considering forming an advisory council that would be composed of leading democracy advocates and presidential hopefuls.
Ganzouri warned that Egypt might become "a new Somalia" if the current situation continued.
Meanwhile, presidential candidate Muhammad ElBaradei has offered to lead a government of national unity, adding fresh pressure on Egypt's ruling generals.
ElBaradei held talks on November 26 with the head of the military council, Hussein Tantawi, state television reported.
In Brussels, the European Union's foreign policy chief Catherine Ashton said she was concerned by the situation in Egypt.
compiled from agency reports