On the heels of his speech, Egyptian opposition groups also rejected offers made by Mubarak for dialogue and would not discuss anything with the newly appointed government until he resigns.
Mubarak, who said he would oversee the transition during the next eight months, added that he would continue to "supervise" the new government to ensure a peaceful transfer of power.
An official with top opposition leader Mohamed ElBaradei, former head of the U.N. nuclear watchdog group who has been championing change in Egypt, told The Washington Examiner
that the opposition "will accept nothing less than Mubarek's resignation."
Muslim Brotherhood spokesman Assam al-Arian told the BBC on Tuesday, "We are rejecting any negotiations or any dialogue with those surrounding Mubarak." The Muslim Brotherhood is also part of the Committee for Change, a coalition of political opposition groups.
Protesters set up their own security checkpoints in Tahrir Square on Tuesday, searching for supporters of Mubarak who were rumored to be hiding weapons in an attempt to disrupt the gathering.
Barbara Ibrahim, founding director of the John D. Gerhart Center for Philanthropy and Civic Engagement at the American University in Cairo, said it was clear that people at the march wanted Mubarak out immediately.
She said the protesters were united in their goals. "There was such a spirit in the square. People were collecting trash, young people were handing out food and there was a solidarity that was extremely rare in Egypt," said Ibrahim, whose husband, Saad Eddin Ibrahim, is a renowned scholar and Egyptian opposition leader.
There was no violence during the protests, she said in a telephone interview with The Examiner from Tahrir Square. "Even though the army had posts around the square, it was the people who were organizing and taking care of one another,"
James Carafano, senior defense analyst with the Heritage Foundation, a Washington-based think tank, said, "The question is, have Mubarak's people worked out a deal with the army?"
"If he's cutting a deal with the army then his decision to stay in office will carry different weight," Carafano said.
Mubarak did not mention the army's role in his speech. Many anti-Mubarak Egyptians believe that the army has shifted to the side of the protesters.
"It would seem like the army is siding with the people," Ibrahim said. "This is the perception many of us have in Egypt. Mubarak is losing ground."
Sara A. Carter is The Washington Examiner's national security correspondent. She can be reached at email@example.com.