Amanpour was granted an exclusive interview with Egypt's new vice president, Omar Suleiman. While at the presidential palace, Amanpour asked to meet with President Hosni Mubarak. She was quickly granted an interview.
He said he felt strong and that he was relieved he had made his decision and that speech on Monday to step down.
Mubarak said he is fed up with being president and would like to leave office now, but cannot, he says, for fear that the country would sink into chaos.
"I don't care what people say about me. Right now I care about my country, I care about Egypt," Mubarak told Amanpour.
Violence continued to rage in the streets of Cairo Thursday as pro-democracy demonstrators continued to clash with supporters of President Hosni Mubarak.
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An increased number of Egyptian soldiers Thursday tried to gain control over protesters, to no avail.
At least 10 people were killed and 100 injured Wednesday after supporters of the president attacked demonstrators.
The Egyptian government has vowed to investigate the violent attacks.
Foreign journalists have come under attack by supporters of the president, angry over television coverage.
More than 20 journalists have been assaulted. Two dozen have been detained.
U.S. Secretary of State Hillary Clinton and United Nations Secretary-General Ban Ki-moon have condemned the attacks on journalists and peaceful demonstrators, saying Egypt's government must provide protection.