Update 4:12 p.m. ET: In a taped address to the Egyptian people, President Hosni Mubarak, 82, said he intends to serve the remaining months of his term so he can oversee a peaceful transition to a new government.

Mubarak said he would not run in the election, which is scheduled for September. Until then, he said, "my main responsibility is to restore order to achieve an easy transition in a peaceful atmosphere."

Msnbc.com has a full report. 

Update 4:07 p.m. ET: "The Hosni Mubarak that is talking to you now is honored for the years that he served the Egyptian people. ... History will judge me."

Update 4:07 p.m. ET: Mubarak says he intends to remain through the end of his term. The next elections are scheduled for September. 

Update 4:05 p.m. ET: Mubarak says he never intended to run for re-election and calls on Parliament to allow court appeals of the disputed November elections to go forth.

Update 4:03 p.m. ET: "My main responsibility is to restore order to achieve an easy transition in a peaceful atmosphere."

Update 4 p.m. ET: "What has hurt the most is the fear that has reached the majority of Egyptians," Mubarak says, according to an interpreter. "The events of Tunisia have been on everyone's mind."

Update 3:58 p.m. ET: Mubarak is speaking.

Update 3:47 p.m. ET: As he did in his address last week, Mubarak has pre-recorded the address he will be giving this evening, NBC News reports.

Update 3:10 p.m. ET: NBC News' Andrea Mitchell reports that the National Security Council is waiting for Egyptian President Hosni Mubarak and will then determine what President Barack Obama may or may not say.

Mitchell reports details of U.S. discussions with Mubarak here: U.S. tells Mubarak he must go 

Update 3:04 p.m. ET: NBC News, The Associated Press and Reuters are all now reporting that Frank Wisner, whom the United States sent to Cairo, told Mubarak that he must find a way to leave the scene. 

Update 3:01 p.m. ET: NBC News' Ron Allen reports from Cairo that Mubarak will speak in 10 to 15 minutes.

Update 2:49 p.m. ET: Egyptian state television says Mubarak will make an "important statement"shortly. 

Update 2:10 p.m. ET: The New York Times, citing American diplomats, reports that President Barack Obama has urged Egyptian President Hosni Mubarak not to seek another term in the September elections.

Update 2:07 p.m. ET: NBC News' Chuck Todd confirms CNN's report that Secretary of State Hillary Rodham Clinton and other national security advisers have been called to the White House for a meeting on Egypt at 3:30 p.m. ET. 

Update 1:57 p.m. ET: CNN reports that President Barack Obama is calling Secretary of State Hillary Rodham Clinton and other national security advisers to the White House for a meeting on Egypt.

Update 1:50 p.m. ET: NBC News says it has confirmed that President Hosni Mubarak will address the nation tonight and will offer an unspecified "good solution."

Update 1:43 p.m. ET: NBC News' Cairo bureau stresses that the Al-Arabiya report that President Hosni Mubarak will address the nation and announce he is not running for re-election in September is unconfirmed.

A source at the Presidential Palace tells NBC that Mubarak "may" make a speech tonight.

Update 1:34 p.m. ET: The Egyptian site Al-Arabiya tweets, citing "reports," that President Hosni Mubarak will announce today that he will not run in the upcoming elections.
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Reuters reports: 

Egypt's President Hosni Mubarak will give a speech on Tuesday after at least 1 million people rallied across the country clamouring for him to step down, Al Arabiya television said. There was no official confirmation.

The channel also said Vice President Omar Suleiman had started meetings with representatives of parties.

Egyptian special forces secure the main floor Monday inside the Egyptian Museum in Cairo.

The Egyptian government says Egypt's museums and ancient monuments, including the Pyramids, are now safe.

Zahi Hawass, the antiquities minister in President Hosni Mubarak's new government, posted an update on his personal Web site this morning that the military had begun safeguarding the nation's heritage sites:

The commanders of the army are now protecting the Egyptian Museum, Cairo,and all of the major sites of Egypt (Luxor, Aswan, Saqqara, and the pyramids of Giza) are safe. The twenty-four museums in Egypt, including the Coptic and Islamic museums in Cairo, are all safe, as well. I would like to say that I am very happy to see that the Egyptian people, young and old, stood as one person against the escaped prisoners to protect monuments all over the country. The monuments are safe because of both the army and the ordinary people.

Some foreigners think Egypt is not interested in protecting our monuments and museums, but that is not true, at all. Egypt has 5,000 years of civilisation, and we love our heritage. I want to send a message to the people of Egypt: all of you are responsible, to ultimately be judged by your own history, to protect your monuments, and should not permit ignorance or outlaws to damage our history – it is the most important thing we own. I am sure the bells from the churches are ringing now, and the voices from the minarets of mosques are calling, to say that Egypt is a safe place to live.

Last week, Bedouins pulled up in a truck and looted a storage site in Qantara, near the Suez Canal, but Hawass writes that 288 objects — " the majority of what was stolen" — have now been returned. 

For the first time, the United States has acknowledged speaking with opposition leader Mohammed ElBaradei.

The notice came in a tweet this morning from P.J. Crowley, the chief spokesman for the State Department:

Twitter.com

The New York Times reports that the United States is trying to determine whether ElBaradei, who won the Nobel Peace Prize as head of the U.N. nuclear agency, is someone it can work with:

Mr. ElBaradei, 68, had a fractious relationship with the Bush administration, one so hostile that Bush officials tried to get him removed from his post at the atomic watchdog agency. But as Egypt’s powerful Muslim Brotherhood and the secular opposition on the streets of Cairo have increasingly coalesced around Mr. ElBaradei to negotiate on their behalf, the Obama administration is scrambling to figure out whether he is someone with whom the United States can deal.

Egyptian opposition leader Mohammed ElBaradei says Egyptians are upbeat for the time being because their message is getting out. At the same time, he tells NBC News' Brian Williams, they "hate the image that is being sent around the world of the looting, the pictures. ... It's been turned upside down this week."

Emilio Morenatti / AP

Protesters shout slogans Tuesday as they march toward Tahrir square in Cairo.

 Hundreds of thousands of people packed Cairo's Tahrir Square to call for reform. See dramatic new images in an msnbc.com slideshow.