The announcement came as hundreds of thousands rallied in central Cairo urging him to step down immediately.
The demonstration was the biggest since protests began last week.
The BBC’s Jim Muir, among the protesters in Cairo’s Tahrir Square, says the crowd erupted in jubilation after hearing the president’s speech.
‘New Egyptian reality’
Mr Mubarak said he would devote his remaining time in power to ensuring a peaceful transition of power to his successor.
“My first priority is to restore peace and stability in our country, to ensure the peaceful transition of leadership, and to ensure that the responsibility goes to whomever the people of Egypt choose in the next election. I do not intend to stand for election again,” he said.
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Crowds in Tahrir Square, Cairo, 1 February 2011
But he criticised the protests, saying what began as a civilised phenomenon turned into a violent event controlled by political cowards.
“The events of the past few days require us all – people and leaders – to make the choice between chaos and stability, and dictate new conditions and a new Egyptian reality,” he said.
He said he had offered to meet all parties but some political powers had refused dialogue.
Opposition politician George Ishak told the BBC expressed dismay at the speech.
“We are very disappointed and we are very angry. We have very clear demands and he denied everything that we demanded. He has to go now. I am afraid now of what will happen in the future,” he said.
Leaders of the protests had called on Mr Mubarak to step down by Friday, when demonstrators were planning to march on the presidential palace.
Journalists in the square estimated hundreds of thousands of people had joined the protest by its peak mid-afternoon.
Correspondents say that hours after dusk and despite a theoretical 1500 (1300 GMT) curfew and bitter cold there were still large crowds, though many people had drifted home.
Many carried placards and banners daubed with anti-Mubarak slogans.