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. 

Felipe Trueba / EPA

Protesters carry a tired comrade over their heads Tuesday in Tahrir Square in Cairo. Click the photo for a slideshow of new images from Egypt.

Vice President Omar Suleiman's announcement of constitutional and electoral reforms doesn't appear to be assuaging the hundreds of thousands of Egyptians packing Tahrir Square today in what reporters on the scene are calling the biggest demonstration since the protests began Jan. 25.

An Al Jazeera correspondent reported that "the vice president came out about 10:30 this morning and said the president had signed a decree allowing for constitutional amendments. ... But I don’t think it worked well. I don’t think anyone here has bothered listening to that yet. The call here is for an end to the regime of the past 30 years and to make sure they will not return once it’s over." 

There are calls for another million man march on Friday; they do not want those that died in the first week to be forgotten. They already have huge posters of those killed in those clashes — and they are planning some kind of memorial service to mark those who have fallen.

They want to keep Tahrir Square as a reminder of the very serious actions that have happened here, and discourage people from just coming down to sightsee and just walk around for a few hours.

Prime Minister Ahmed Shafiq says President Hosni Mubarak won't step down before September, according to MSNBC TV's translation of his interview today on Egyptian state TV.

"We as civilized people must honor the president, who did a good job regardless of mistakes here and there," Shafiq said. "Today the Egyptian people see that the president will not step down."

Shafiq also said it's unlikely that Mubarak would turn power over to Vice President Omar Suleiman, saying, "I doubt that this is acceptable."

But a resolution of some sort, which he did not outline, is in the works soon, he said.

"We are approaching the agreements points. There are more points that need to be discussed," he said, according to MSNBC. "Both sides must give concessions so we can meet halfway."

More from the interview:

• "This movement achieved lot of their demands. ... I think this movement is a positive movement."

• "The president said he will leave power next September, and if you look at it, it's only five months. ... We as civilized people must honor the president, who did a good job regardless of mistakes here and there."  • "President Mubarak  ... did not make the mistakes. There were wrongdoings by the Cabinet — that's why you see changes."

• "Let us be comfortable that he decided to give up power in September. We see his place in power as a safety valve."

Update 2:33 p.m. ET: A senior U.S. official says evidence like the comments below confirms that "there is a debate going on inside the inner circle."

Speaking to NBC News' Courtney Kube, the official declined to speculate whether the members of that "inner circle" are influential enough — and the disagreements strong enough — to force Mubarak to step down, saying only that the current situation is "just not sustainable."

Even without the rumblings within the government, "the economy continues to grind down," which could force a resolution sooner rather than later, the official said.

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While some government ministers are reported to be joining protesters in Tahrir Square, others appear to be falling in line behind President Hosni Mubarak.

The Middle East network Al Arabiya reports that Prime Minister Ahmed Shafiq predicts that Mubarak probably wouldn't turn over power to Vice President Omar Suleiman. "We need the president for legislative reasons," Al Arabiya quotes Shafiq as saying on state television.

(The undetailed report was picked up by Reuters; MSNBC TV is reviewing a tape of Shafiq's comments and will have more shortly.)

Meanwhile, Hala Gorani of CNN International says in a series of tweets that she has interviewed Foreign Minister Ahmed Abul Gheit, who said Mubarak would try to stay in office through the elections:

"Abul Gheit said outside forces cannot dictate transition of power. Plan is still for Mubarak to stay on til Sept."

Update 4 p.m. ET: Der Standard has edited its story to remove the passage in which it quoted ElBaradei as saying he would not run. It says in an accompanying note that "our interview with Mohamed ElBaradei on Friday afternoon was conducted under quite difficult circumstances and in great haste" and says it has "corrected" the  story in light of ElBaradei's later comments.

Update 1:21 p.m. ET: Reuters reports that ElBaradei has told Al Jazeera that he might, in fact, run for president "if the Egyptian people want me."

Addressing the Standard report below, ElBaradei said by telephone that "this is not true," Reuters says. 

Reuters translates Der Standard's interview transcript very similarly to the msnbc.com translation below:

"No, I will not take part. The best I can do is act as an agent for change," Reuters quotes in its translation. "Naturally I want to play a part in the future, but who stands in the election, that's really not so important at the moment."

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Opposition leader Mohamed ElBaradei is quoted in an interview with an Austrian newspaper as saying he won't run for president.

"No, I will not run," Der Standard of Vienna quotes ElBaradei, who won the Nobel Peace Prize for his work as head of the U.N. nuclear agency, as saying in a telephone interview. "The best I can do to be an agent for change is to act as one. I am an agent of change."

It's not unexpected that this report would be in an Austrian newspaper. ElBaradei  was based for many years in Vienna, where the International Atomic Energy Agency has its headquarters.

You can read the interview here, in German. 

Other key points, as translated by msnbc.com:

• "I stand above parties, which gives me more flexibility to express myself clearly. Of course I want to be involved in the future of Egypt, but whoever runs in elections right now is really not that important."

• "Many young protesters see [Vice President Omar Suleiman] as just an extension of [President Hosni] Mubarak. There is great opposition to him. But I think all these issues can be resolved if Mubarak steps down."

• "If he's ready to go, we would ensure a dignified departure — this can be arranged. He has done many bad things, but he has also done good things for this country. ... He should step down with dignity."