Embattled Morsi looked increasingly isolated, with his Foreign Minister Mohamed Kamel Amr resigning on Tuesday to take the number to five. On Monday, four other ministers resigned.
"The civil democratic Egyptian state is one of the most important achievements of the January 25 revolution," said a statement from the presidency, referring to the 2011 pro-democracy protests that toppled longtime ruler Hosni Mubarak.
"Egypt will absolutely not permit any step backward whatever the circumstances," the statement added.
The powerful army on Monday warned that it will intervene if people's demands were not met within 48 hours after millions took to the streets asking Morsi to quit.
Morsi, 61, is first freely elected president of Egypt. He assumed charge a year ago after Egyptians overthrew Mubarak, an authoritarian and military-backed leader.
"If the demands of the people are not met in this period... (the armed forces) will announce a future roadmap and measures to oversee its implementation," said the army statement, which was read out on television.
However, the presidency said that the army declaration had not been cleared by it. It also denounced any declaration that would "deepen division" and "threaten the social peace".
Morsi was consulting "with all national forces to secure the path of democratic change and the protection of the popular will", the presidency said.
The army, however, in a new statement on Tuesday said its motive was to find a speedy solution to the situation. The statement, which was posted by the army on its Facebook page, said: "the creed of the Egyptian Armed Forces does not allow it to perform a coup d'etat and was issued to force politicians to find a speedy solution for the deadlock."
"The armed forces are neither the ruler nor part of the political scene and will not abandon its designated role." Morsi's opponents accuse him of putting the Brotherhood's interests ahead of the country's as a whole.