He said he's 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 was very unhappy about yesterday. I do not want to see Egyptians fighting each other," he said of the violence, which, by most accounts, was provoked by Mubarak supporters that may have included plainclothes police officers, government employees and people paid to attend the rallies.
Asked how he felt about President Obama's suggestion that he step aside soon, Mubarak said he told Obama, "You don't understand the Egyptian culture and what would happen if I step down now."
"I never intended to run again. I never intended Gamal [his son] to be President after me," he said.
Mubarak and his family, Amanpour reports, are holed up in the presidential palace in Cairo, which is surrounded by soldiers and barbed wire.
There's no video, yet, of the interview. But here's Amanpour describing the meeting on ABC:
Dozens of journalists have been harassed, threatened, attacked and detained by Mubarak supporters, the army and protesters on both sides over the past few days.
Amanpour and her crew had a confrontation yesterday with Mubarak supporters, where they told her to leave the area.