Editor's note: Read the full text of President Barack Obama's Thursday-night statement on Egypt.
(CNN) -- President Barack Obama signaled clear support for protesters who have convulsed Egypt, saying Thursday night that "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."
In a White House statement following a previously unscheduled meeting of Obama with this national security team, the president called President Hosni Mubarak's speech earlier in the night that announced he would hand over presidential authority to his vice president but remain in office both confusing and insufficient.
"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," Obama said in the statement, later adding that the Egyptian government "must put forward a credible, concrete and unequivocal path toward genuine democracy, and they have not yet seized that opportunity."
He urged 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 bystep process that will lead to democracy and the representative government that the Egyptian people seek," according to the statement.
Obama also said in the statement that it was "imperative" that the Egyptian government "not respond to the aspirations of their people with repression or brutality."
The president's statement was the only official U.S. response to Mubarak's speech on state television that infuriated tens of thousands of demonstrators in the streets of Cairo, raising concerns of larger and potentially volatile protests on Friday.
Obama watched Mubarak's speech on Air Force One on the return flight from a speech in Michigan, according to White House Press Secretary Robert Gibbs. Once back at the White House, Obama met with the national security team, Gibbs said.
Earlier in the day, as reports circulated that Mubarak would announce he was stepping down in response to more than two weeks of growing protests that have convulsed Egypt, Obama said the world was "witnessing history unfold."
In comments at the start of his Michigan speech, Obama called the situation in Egypt "a moment of transformation taking place because the people of Egypt are calling for change."
He repeated the persistent U.S. call for an "orderly and genuine transition to democracy in Egypt."
Mubarak's refusal to step down caught the administration off guard, a senior U.S. official told CNN on condition of not being identified by name.
"Not what we were told would happen and not what we wanted to happen," the official said of the speech.
Confusion over what Mubarak would say was apparent beforehand. CIA Director Leon Panetta told a U.S. congressional committee earlier Thursday that there was a "strong likelihood that Mubarak may step down this evening, which would be significant in terms of where the hopefully orderly transition in Egypt takes place."
"I don't know the particulars of how this would work, but I would assume that he would turn over more of his powers to (Vice President Omar) Suleiman to direct the country and direct the reforms that will hopefully take place," Panetta said.
House Minority Leader Nancy Pelosi, D-California, said that if the reports of Mubarak's pending resignation were true, then "it would certainly be a victory for the young people who had the courage to demonstrate for democratic freedoms in Egypt. I congratulate them on their success. I salute them for their courage. Their energy changed -- is changing -- Egypt. Their actions are an inspiration to the world."
Obama was briefed by National Security Adviser Tom Donilon in the Oval Office on Thursday morning before he left to travel to Michigan, and watched news of what was happening in Egypt on the flight out, Gibbs said.
Gibbs was reluctant to weigh in on the developments in the morning, saying repeatedly: "We're watching a very fluid situation."
Administration officials and other sources, including Egyptian officials, had provided various scenarios for what might happen. Possible outcomes included Mubarak turning over power to Suleiman; Mubarak turning over power to the military; and Mubarak refusing to step aside.
At the congressional hearing, Panetta reiterated the crucial role of the military.
The loyalty of the military is now something we have to pay attention to because it is not always one that will respond to what a dictator may or may not want," Panetta said.
Key Egyptian government officials have sought to portray an immediate departure by Mubarak as a recipe for absolute mayhem and have warned of military intervention.
That could lead to a "dangerous" situation, Egyptian Foreign Minister Ahmed Aboul Gheit said in two interviews Wednesday, with PBS' "NewsHour" and Al-Arabiya television.
"Do we want the armed forces to assume the responsibility of stabilizing the nation through imposing martial law and the army in the streets?" Gheit said on PBS. "For the army to rule, to step in, to put its friends on the scene, that would be a very dangerous possibility."
A senior Egyptian government official had told CNN on Thursday that Mubarak was expected to announce he would transfer power to the military.
The move would take Egypt's government outside "constitutional authority," the official said.
"This is not a coup in the traditional sense," the official said. "But this is a transfer of the system of government from the civilian to military. The military is stepping up, recognizing its responsibility to the Egyptian people."
The official added that there was a consensus between the government and the military that a political transition was impossible with Mubarak in power.
The United States provides more than $1.3 billion in military aid to Egypt each year, according to the U.S. State Department website.
If Mubarak were to turn over power to a military council, the United States will have to determine legal and diplomatic arrangements for working with a new Egyptian military-led government, a senior U.S. official said.
"It will all have to be determined," the official said, adding that the issues that could be problematic include all security arrangements as well U.S. military sales to Egypt, bilateral training exercises, the transit of the Suez Canal, and arrangements for operations in Sinai along the Gaza border.
However, another senior U.S. official said the legal trigger for ending cooperation only kicks in when the military takes over a democratic country, which would not be the case in Egypt.
CNN's Jill Dougherty, Elise Labott, Jamie Crawford, Deirdre Walsh, Shawna Shepherd, John King, Barbara Starr and Tom Cohen contributed to this story.