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.
But he criticised the protests, saying what began as a civilised phenomenon turned into a violent event controlled by 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.
"This is my country. This is where I lived, I fought and defended its land, sovereignty and interests, and I will die on its soil," he said.
Opposition politician George Ishak 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 told the BBC.
Leaders of the protests had called on Mr Mubarak to step down by Friday, when demonstrators were planning to march on the presidential palace.


Army vow
Mr Mubarak's speech came after a meeting with US special envoy Frank Wisner, who was said to have urged the president to announce his departure.
While this address would have been acceptable a week ago, US officials believe that it is now too little too late and Mr Mubarak should leave now. Many protestors carried placards and banners daubed with anti-Mubarak slogans. Egypt's powerful army has vowed it will not use force against the protesters, despite maintaining a strong presence in central Cairo.