He's offered to hold talks with opposition leaders but as CBS Evening News anchor Katie Couric reports, but today many of those leaders said they will not come to the table until Mubarak is gone.
The backdrop of violence in Cairo only underscores the long road ahead for Egypt. Mohammed ElBaradei, former head of the International Atomic Energy Agency and one of the lead negotiators for the opposition - says working with Mubarak is non-negotiable. "I will never get into a dialogue," he said, "while Mubarak is in power."
Complete Coverage: Anger in the Arab World
"Because all what you do is give that regime a legitimacy, which in my view, they have lost," he added. "But more importantly - I don't think he understand what democracy means. I don't think he understands that he really needs to, you know, let go."
ElBaradei says there would be no power vacuum if Mubarak were to leave immediately. He believes that stoking fears about what a new Egypt might look like is a ploy by the current government.
"The hype that once Egypt becomes a democracy, it will become hostile to the U.S. and hostile to Israel - I mean, these are the two hypes and are fictions," he said.
But Ibrahim Kamel, a close confidant of Mubarak's, says he is concerned about an extremist power grab and insists the majority of Egyptians support the president and want to give him time.
"90 percent of Egyptians will tell you that President Mubarak represents for Egypt something very valuable," Kamel said. "They stand behind him. They believe that by the end of his term - the changes that will take place in our political system will make Egypt a much better place for the future."
Whatever lies ahead for Egypt, Amr Moussa, the head of the Arab League, which represents 22 Arab nations, says there is no turning back for Egypt or the rest of the Arab world.
"The message has been sent, the message has been received - it will never be the same again," Moussa said. "I firmly believe that the Arab world in one year's time will not be the same as it is today."