(CNN) -- Thousands of people waved Egyptian flags and roared, "Get out! Get out!" in Cairo's Tahrir Square as President Hosni Mubarak said late Thursday he was delegating power to his vice president and made no mention of stepping down.
"I don't know if he has a brain or if his brain is elsewhere," one protester in the square said, expressing frustration that Mubarak appeared to be saying that he enjoyed support from most Egyptians.
Watching Mubarak's address on what appeared to be a sheet hoisted over the square, the crowd became angry as they heard Mubarak say he would "delegate powers" to Vice President Omar Suleiman but did not mention leaving office. They broke into cries of, "Illegitimate!" and "Mubarak the coward must stand down."
After the statement, parliamentary speaker Ahmed Fathi Srour told Nile TV that Mubarak's move had put the authority for the day-to-day running of the government in Suleiman's hands. That would include oversight of the police, the interior ministry and other key agencies, as well as control of economic policy and running any negotiations with opposition figures.
Srour added that the constitution specifically prohibits the president from delegating certain key powers to the vice president, including the power to dismiss parliament or dismiss the government and the power to ask for amendments to the constitution.
"The vice president is the de facto president," said Sameh Shoukry, Egypt's ambassador to the United States.
Mubarak's stance did not appear to satisfy many protesters in Tahrir Square.
"A lot of people ... said Mubarak was going to do what the people want. That means he's going to resign. After that speech, we find he's not going to resign," a second demonstrator told CNN.
After the speech, hundreds of anti-government demonstrators went toward Egypt's presidential palace, and by early Friday morning were sitting behind barbed wire outside the building, with several tanks positioned behind the wire. The palace is about six miles from Tahrir Square.
A house of Mubarak is situated about 100 meters (328 feet) from the palace.
Demonstrators had also gathered early Friday in front of the offices of state-run Nile TV, which has been seen as a mouthpiece for the Mubarak administration.
In northern Alexandria, hundreds marched late Thursday toward an Egyptian military base to express their anger that Mubarak had not stepped down, said Yaser Fathi, an organizer of demonstrations in that port city. The protesters voiced their opposition to both Mubarak and Suleiman, and urged the military to act.
"The military must step in to get Mubarak out," the group chanted, according to Fathi.
The crowd in Cairo's Tahrir Square was largely still for the first several minutes of Mubarak's address. The crowd had stood vigil all day in the square, which has become the epicenter of the protests.
Several sources, both in Egypt and abroad, had said Mubarak would announce his resignation during the late-night address. But the president repeatedly said he would not bow to foreign pressure, which seemed to imply that calls for his resignation were coming from beyond Egypt's borders.
At the square, the first protester who'd spoken to CNN was asked if he was angry.
"Of course we are! We all are!" he replied.
"He is saying that he wants to keep the country in one piece and wants to keep the country safe, and dignity and this, blah blah blah blah," said the protester. "He just (is) talking from a different island. He is ruling another country."
Another demonstrator said, "Mubarak , game over. ... We want him to step down. We don't trust him anymore, and the problem is not Mubarak. The problem is the gangsters around him."
One man described Mubarak's speech as "useless." He said he and others were "ready to die for freedom," and said Egyptians would continue their protests until Mubarak stepped down.
"All the people ... are looking for freedom, justice and to be respected," he said. "We will have justice, we will have freedom, and we will live as human beings in this life."
Another demonstrator said people, anticipating before the speech that Mubarak was about to resign, had been ready to leave Tahrir Square.
"If he stepped down like lots of people wanted, some of the people who are sitting here in Tahrir Square (were) going to leave to their homes," he said. "We're staying here. We're not leaving until he leaves."
A small tent city has emerged in the square, with some protesters starting to construct shelters out of plywood. Many have said they will not leave the square until Mubarak is no longer president, with many insisting he leave Egypt altogether.
CNN's Frederik Pleitgen and Saad Abedine contributed to this report.