The statement by the Armed Forces Supreme Council - its second in two days - was a blow to many protesters who had called on the military to take action to push out Mubarak after his latest refusal to step down.
But soldiers also took no action to stop demonstrators from massing outside the palace and the headquarters of state television, indicating they were trying to avoid another outbreak of violence.
Anti-government protesters said they were more determined than ever as the uprising entered its 18th day.
"We expected the army's decision, we always knew that it was behind Mubarak. But we know it's not going to harm us," Safi Massoud said as she joined thousands of people packed into Cairo's central Tahrir Square. "We wont leave until we choose a transition president. We don't want Mubarak, we don't want Suleiman."
The military statement endorsed Mubarak's plan to transfer some powers to Vice President Omar Suleiman and promised free and fair presidential elections later this year.
It also promised that the hated emergency laws, in force since Egypt's authoritarian ruler came to office in 1981, would be lifted and gave a somewhat more specific timeframe than Mubarak had offered in his Thursday night speech.
The military implied they would be lifted when protests end, saying it could happen "when the current security situation permits."
It also called for public services to resume and urged "the return of normal life in order to safeguard the achievements of our glorious people."
Undaunted, thousands packed into Cairo's central Tahrir Square, or Liberation Square, which has been the center of the uprising since it began on Jan. 25.
A few hundred protesters assembled outside the gate of Mubarak's Oruba Palace. The palace was protected by four tanks and rolls of barbed wire, but soldiers were doing nothing to stop demonstrators from joining the rally and chanting anti-Mubarak slogans.
Others massed outside the Cabinet, parliament and the state television headquarters several blocks away from Tahrir Square, the center of the mass rallies that began on Jan. 25.
Hundreds of demonstrators formed a human barricade around the building that houses state TV and radio, checking IDs and turning away those who work there. Tanks and barbed wire surrounded the building overlooking the Nile, but troops did not keep protesters away.
Hopes that Mubarak would resign had been raised Thursday when a council of the military's top generals announced it had stepped in to secure the country, and a senior commander told protesters in Tahrir Square that all their demands would soon be met.
Instead, several hundred thousand people watched in disbelief and anger as Mubarak refused to step down.
Mubarak called the protesters' demands legitimate and promised that September presidential elections - in which he says he will not run - will be "free and fair" with supervision to ensure transparency.
He said that on the recommendation of the panel, he had requested the amendment of five articles of the constitution to loosen the now restrictive conditions on who can run for president, to restore judicial supervision of elections, and to impose term limits on the presidency.
He also annulled a constitutional article that gives the president the right to order a military trial for civilians accused of terrorism. He said that step would "clear the way" for eventually scrapping the emergency law but with a major caveat - "once security and stability are restored."
The emergency law gives police virtually unlimited powers of arrest.
Prominent reform advocate Mohamed ElBaradei, whose supporters were among the organizers of the 18-day-old wave of protests, called in a Twitter message on the army to step in "to rescue Egypt," warning the country might "explode."
Another leading figure of the protest movement, Google executive Wael Ghonim, called for caution.
"The situation is complicated. I don't want the blood of the martyrs to be wasted and at the same time I don't want to see more bloodshed," he said in comments posted on Facebook.
The Muslim Brotherhood, Egypt's largest and best organized opposition group, called the speech a "farce."
"This is an illegitimate president handing power to an illegitimate vice president," said Mohammed Abbas, who represents the Brotherhood's youth wing. "We reject this speech and we call on Mubarak to step down and hand his powers to the army."
In his address on state TV, Mubarak showed the strategy he has followed throughout the days of upheaval, trying to defuse the greatest challenge ever to his nearly three-decade authoritarian rule. So far, he has made a series of largely superficial concessions while resolutely sticking to his refusal to step down immediately or allow steps that would undermine the grip of his regime.
Looking frail but speaking in a determined voice, Mubarak spoke as if he were still in charge, saying he was "adamant to continue to shoulder my responsibility to protect the constitution and safeguard the interests of the people." He vowed that he would remain in the country and said he was addressing the youth in Tahrir as "the president of the republic."
Even after delegating authority to his vice president, Mubarak retains his powers to request constitutional amendments and dissolve parliament or the Cabinet. The constitution allows the president to transfer his other authorities if he is unable to carry out his duties "due to any temporary obstacle."
"I saw fit to delegate the authorities of the president to the vice president, as dictated in the constitution," he said.
President Barack Obama appeared dismayed by Mubarak's announcement. He said in a statement that it was not clear that an "immediate, meaningful" transition to democracy was taking place and warned that too many Egyptians are not convinced that the government is serious about making genuine change.
Suleiman was already leading the regime's efforts to deal with the crisis, though he has failed to ease the protests, which have only escalated in size and ambition, drawing crowds of up to a quarter-million people.
Suleiman has also offered dialogue with the protesters and opposition over the nature of reforms. In a sign that he is sticking to that strategy, state TV reported that he asked Prime Minister Ahmed Shafiq to appoint a deputy prime minister to be in charge of the dialogue with the protesters and the opposition.
Despite the overwhelming sense of disappointment among the protesters, some noted that Mubarak's immediate resignation would have had unintended consequences. His immediate departure would have triggered presidential elections within 60 days, with most of the restrictions that prevented free voting the past still in place, said Amr Hamzawy, an Egyptian legal expert.
By transferring most powers to Suleiman and initiating constitutional amendments, Mubarak did the maximum possible under the constitution to meet the demands of the protesters, Hamzawy said.
"He went in a direction that is more preferable to open Egyptian politics in the next few months," said Hamzawy.
Associated Press writers Hadeel al-Shalchi and Hamza Hendawi contributed to this report.