Mubarak said he would remain nominally in charge until September, and vowed he would one day die in Egypt rather than seek exile, infuriating protesters.
The reaction was immediate, angry and dismayed.
His televised speech was met with angry chants of "Down, Down with Mubarak" among the more than 200,000 people who packed Cairo's Tahrir Square on the 17th day of massive nationwide protests demanding the strongman's overthrow.
Many of the protesters called for an immediate general strike and angrily addressed the army, which had deployed large numbers of troops and tanks around the square: "Egyptian army, the choice is now, the regime or the people!"
Following the speech, the bulk of the crowd began to disperse, but most vowed to return on Friday, which has already been declared a "day of rage".
A hard core of several thousand protesters was to remain in the sprawling tented encampment that has occupied the square since January 28.
"We won't leave until he leaves," declared 32-year-old accountant Ayman Shawky. "I don't think it's stupidity, it's arrogance. He lost his last chance to leave with his dignity intact."
Hopes had run high that Mubarak would step down immediately after the military leadership had announced hours earlier that it would intervene to ensure the country's security and see that the people's "legitimate" demands were met.
But by the end of his speech Mubarak remained president.
Delegating his powers to his former intelligence chief Suleiman, a frail Mubarak said in a scratchy voice. "I have decided to delegate power to the vice president based on the constitution."
"I am conscious of the dangers of this crossroad... and this forces us to prioritise the higher interests of the nation."
He went on to take a swipe at the United States and other countries that have pushed him to accelerate a transition to democracy, saying: "I have never bent to foreign diktats.
"I have always preserved peace and worked for Egypt and its stability."
Speaking after Mubarak, Suleiman told the protesters to go home.
But as they began peacefully filing out of Tahrir Square, the chants grew darker. "To the palace we are heading, martyrs by the millions!" they shouted.
Earlier, the square had been bathed in a carnival atmosphere, as many tens of thousands of Egyptians gathered to celebrate what they hoped would be Mubarak's final speech of a three-decade-long autocratic reign.
When they realised he was refusing to step down, the mood changed and deep-seated anger rose to the surface.
The crowd chanted "Neither Mubarak nor Suleiman!" as one elderly woman moaned: "The old man just won't give up power."
"He is still speaking to us as if we were fools," said Ali Hassan. "He is a general defeated on the battlefield who will not retreat before inflicting as many casualties as he can."
Earlier, tens of thousands of Egyptian workers striking nationwide had swelled the protesters' ranks, increasing the chances Friday's demonstrations would be the biggest yet.
Immediately after Mubarak's speech, US President Barack Obama called an emergency meeting of his national security team.
Obama watched Mubarak's nationwide address aboard Air Force One, hours after telling a crowd in Michigan that history was unfolding in Egypt, amid rumours and reports at the time that the 82-year-old Arab strongman would step down.
There was no immediate comment from senior US officials on Mubarak's speech and Obama declined to answer shouted questions from reporters after he exited his Marine One helicopter and marched into the Oval Office.
But CNN quoted one unnamed official as saying the speech was "not what we were told would happen, not what we wanted to happen."
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