The Egyptian president, in a televised address from his palace in Cairo, promised a peaceful transfer of power but did not spell out exactly what was next.
He said the demands of protesters calling for his immediate ouster were just, and he said he had requested six constitutional amendments in line with their urging. He said he would lift hated emergency laws when security permitted.
Mubarak also vowed to punish those behind violence over the past two weeks and offered condolences to the families of those killed. He said he was transferring some power to his vice president, Omar Suleiman, but the angry crowd in Cairo's central square clearly was not satisfied.
"We are following today's events in Egypt very closely," President Obama said before Mubarak's speech, adding that he would "have more to say as this plays out."
"What is absolutely clear is we are witnessing history unfold," Obama told students at Northern Michigan University in Marquette, Mich. "It's a moment of transformation."
Mubarak was under enormous pressure from protesters pushing for the immediate end of his 29-year hold on power.
Washington officials followed the unfolding drama in Cairo with hopeful expectation for a smooth transition _ mixed with concern over the unpredictability of the developments.
"There is no question that what we are seeing happening in Egypt will have tremendous impact," Panetta told the House Intelligence Committee. "If it's done right, it will help us a great deal in trying to promote stability in that part of the world. If it happens wrong, it could create some serious problems for us and for the rest of the world."
Obama said that "the people of Egypt are calling for change, they've turned out in extraordinary numbers and all ages and all walks of life." But especially, Obama said, it was young people "who've been at the forefront" of the demand for change.
"We want those young people, and we want all Egyptians to know, America will do all we can to support an orderly and genuine transition to democracy in Egypt," he told his youthful audience. Obama was in Michigan to promote plans to widen access to high-speed wireless services.
On Capitol Hill before Mubarak's speech, House Intelligence Committee Chairman Mike Rogers of Michigan asked CIA Director Leon Panetta about news reports that the leader was poised to relinquish power.
"I got the same information you did, that there is a strong likelihood that Mubarak will step down this evening, which will be significant in terms of where the hopefully orderly transition in Egypt will take place," the CIA director said.
Egypt's military announced on national television that it had stepped in to "safeguard the country" and assured protesters that Mubarak would meet their demands. That was the strongest indication yet that the longtime leader was leaving.
The administration was also watching closely for developments that might affect U.S. aid to Egypt. A coup or other non-constitutional transfer of power could trigger a statutory suspension in all non-humanitarian assistance. The U.S. is providing at least $1.5 billion annually to Egypt in military aid.
Panetta, after his congressional testimony, told reporters that, while "we've received indications that he (Mubarak) was going to make these remarks" to announce he was stepping down, "we haven't been able to confirm that he in fact is going to do that, so we're just monitoring the situation right now."
Director of National Intelligence James Clapper, who appeared with Panetta before the House committee, said the terror syndicate al-Qaida and the Islamic hardline groups Hamas and Hezbollah were also paying close attention to the unfolding events in Egypt.
"They are watching and observing this just as we are and are looking for opportunities perhaps to exploit or further their interests," Clapper said.
In testimony to the House Foreign Affairs Committee, Deputy Secretary of State James Steinberg said the administration has "declared publicly and privately that a peaceful, orderly and meaningful transition must begin without delay."
Both Republicans and Democrats expressed concerns about whether the fundamentalist Muslim Brotherhood would be part of any post-Mubarak government and pressed Steinberg on the administration's position on the group. The officially banned Brotherhood, the largest opposition group in Egypt, advocates rule by Islamic law.
"We are not focused on any one group," Steinberg told the committee.
Steinberg said the administration was actively working to ensure that an Egyptian government strengthens liberties and respects religious groups as well as honors Egypt's peace treaty with Israel.
Rep. Ileana Ros-Lehtinen, R-Fla., chairwoman of the committee, said flatly, "Engaging the Muslim Brotherhood must not be on the table."