Update 3:16 p.m. ET: President Barack Obama has saluted former Egyptian President Hosni Mubarak, who he says has "responded to the Egyptian people's hunger for change."

"There are very few moments in our lives when we have the privilege of witnessing history taking place. This is one of those times," Obama said in a televised address from the White House. "Egypt will never be the same."

Obama thanked the Egyptian military for behaving "responsibly as a caretaker of the state." NBC News reported earlier today that after having promised for more than a week not to act violently against protesters, senior military leaders delivered an ultimatum to Mubarak last night to step down or they would join the protests themselves.

The next step, Obama said, is for Egypt to find a government committed to "protecting the rights of Egyptian citizens, lifting the emergency law and revising the constitution and other laws to make this change irreversible."

If it does, he said, "I know that a democratic Egypt can advance its role of responsible leadership not only in the region but around the world."

"Above all," Obama said, "we saw a new generation emerge ... to call for a government that represents their hopes and not their fears."

"They put a lie to the notion that justice is gained through violence," he said in an address  that was strikingly different in tone from the terse critical statement he issued last night after Mubarak initially refused to step aside.

"Today belongs to the people of Egypt."

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President Barack Obama is about to make a statement on Egypt after a long meeting with his national security team.

The Egyptian military essentially gave President Hosni Mubarak an ultimatum last night, NBC News' Richard Engel reports from Cairo.

Several senior officials were "furious" with Mubarak's refusal to step down and threatened to take off their uniforms and join the protesters, Engel reported.

"When the military comes in and tells the president, 'We will not stand beside you — you must stand down,' it's hard to call it anything but a coup," Engel said.

Click the video for Engel's full report with NBC's Lester Holt.

Update 1:38 p.m. ET: The White House no says President Barack Obama is expected to speak about 3 p.m. ET.

Updated 1:03 p.m. ET: The White House now says  Obama's remarks will come  at a "time to be determined." It previously had said Obama would speak at 1:30 p.m. ET.

Update 11:48 p.m. ET: Reuters is quoting a military source as saying Defense Minister Mohamed Hussein Tantawi is the head of the Higher Military Council that has taken control from Hosni Mubarak.

Update 11:45 a.m. ET: NBC's Richard Engel reports from Cairo that a communiqué from the military — in essence, the new interim ruler of Egypt — is expected at any moment.

Update 11:20 a.m. ET: President Barack Obama will make a televised statement at 1:30 p.m. ET, the White House says. 

The president was told of Mubarak's intention to resign during a meeting and watched the announcement on television, it says. 

Update 11:15 a.m. ET: As word of Mubarak’s resignation spread through Cairo’s Tahrir Square, a raucous celebration erupted among the protesters who have made his departure from power their no. 1 goal.  Mohamed ElBaradei, the Nobel Peace Prize winner who returned to Egypt to join the protests, said, "This is the greatest day of my life. The country has been liberated."

Update 11:03 a.m. ET: Suleiman came out for a few seconds and announced that Mubarak is resigning and that the Supreme Military Council has been appointed to administer Egypt.

The hundreds of thousands of people in Tahrir Square immediately erupted in joyous cheers.

Update 10:29 a.m. ET: NBC News, citing U.S. and Egyptian officials, reports that the message will come from Vice President Omar Suleiman, who the officials said will try to "clarify" exactly what Mubarak's speech meant.

"Obviously, they had that opportunity last night, and it was muddled," a U.S. official said.

Amid widespread reports that President Hosni Mubarak has left Cairo for his home in the resort town of Sharm El Sheikh, Egyptians are awaiting what's being described by state television as an "urgent and important" announcement from the "presidency," NBC's Richard Engel reports from Cairo.

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A White House official called Mukarak's departure for Sharm el Sheikh a "positive first step," but other officials cautioned against reading too much into it, noting that it's been essentially a second full presidential center for years.

Mubarak typically spends a good part of the year in his "rest house" in Sharm el Sheikh, often receiving official guests and convening summits and conferences there, NBC's Charlene Gubash reported from Cairo.

As for the oending announcement, the word "presidency" leaves it unclear whether that would be a message from Mubarak or from Vice President Omar Suleiman, who U.S. officials are increasingly convinced has assumed full presidential authority after Mubarak's ambiguous speech yesterday, NBC's Jim Miklaszewski reports from Washington.

In fact, it's unclear exactly what role Mubarak could play except to officially hang on to his title, a U.S. official said this morning, adding, "There are nuances to this that we still don't understand."

The German government told NBC News that it hasn't gotten any "official request from the Egyptian government for Mr. Mubarak to come to Germany," referring to widespread speculation last week that Mubarak might be headed to a health clinic in Baden-Baden. 

The White House has just issued this statement from President Barack Obama:

The Egyptian people have been told that there was a transition of authority, but it is not yet clear that this transition is immediate, meaningful or sufficient. Too many Egyptians remain unconvinced that the government is serious about a genuine transition to democracy, and it is the responsibility of the government to speak clearly to the Egyptian people and the world. The Egyptian government must put forward a credible, concrete and unequivocal path toward genuine democracy, and they have not yet seized that opportunity.

As we have said from the beginning of this unrest, the future of Egypt will be determined by the Egyptian people. But the United States has also been clear that we stand for a set of core principles. We believe that the universal rights of the Egyptian people must be respected, and their aspirations must be met. We believe that this transition must immediately demonstrate irreversible political change, and a negotiated path to democracy. To that end, we believe that the emergency law should be lifted. We believe that meaningful negotiations with the broad opposition and Egyptian civil society should address the key questions confronting Egypt's future: protecting the fundamental rights of all citizens; revising the Constitution and other laws to demonstrate irreversible change; and jointly developing a clear roadmap to elections that are free and fair.

We therefore urge the Egyptian government to move swiftly to explain the changes that have been made, and to spell out in clear and unambiguous language the step by step process that will lead to democracy and the representative government that the Egyptian people seek. Going forward, it will be essential that the universal rights of the Egyptian people be respected. There must be restraint by all parties. Violence must be forsaken. It is imperative that the government not respond to the aspirations of their people with repression or brutality. The voices of the Egyptian people must be heard.

The Egyptian people have made it clear that there is no going back to the way things were: Egypt has changed, and its future is in the hands of the people. Those who have exercised their right to peaceful assembly represent the greatness of the Egyptian people, and are broadly representative of Egyptian society. We have seen young and old, rich and poor, Muslim and Christian join together, and earn the respect of the world through their non-violent calls for change. In that effort, young people have been at the forefront, and a new generation has emerged. They have made it clear that Egypt must reflect their hopes, fulfill their highest aspirations, and tap their boundless potential. In these difficult times, I know that the Egyptian people will persevere, and they must know that they will continue to have a friend in the United States of America.