Mr. Morsi came to power as Egypt's first democratically elected president following Mr. Mubarak's departure in 2011.
His Muslim Brotherhood movement was designated by the interim government as a terrorist group following the September bombing of a security directorate in Mansoura, a town north of Cairo, in which 15 were killed.
The al-Qaida-linked group Ansar Beit al-Maqdis claimed responsibility for the bombing in Mansoura and other attacks, saying they were carried out to avenge the military-backed government's crackdown on Islamists.
U.N. Secretary-General Ban Ki-moon condemned Friday's explosions in the Cairo area as "terrorist attacks." He said no cause could justify such acts.