His comments in a national TV address confounded earlier reports that he was preparing to stand down immediately.
Mr Mubarak said he would delegate some powers to Vice-President Omar Suleiman, but would ignore “diktats from abroad”.

Thousands of anti-government protesters in Cairo’s Tahrir Square reacted angrily to his announcement.
Mr Mubarak had already pledged not to stand in September’s poll.
“I express a commitment to carry on and protect the constitution and the people and transfer power to whomever is elected next September in free and transparent elections,” Mr Mubarak said.
Directly addressing protesters “in Tahrir Square and beyond” in what he said was “a speech from the heart”, Mr Mubarak, 82, said: “I am not embarrassed to listen to the youth of my country and to respond to them.”

He apologised to the families of protesters killed in clashes with the security forces in recent weeks, and said those responsible for their deaths would be punished.
He added that the country’s emergency laws would only be lifted when conditions were right.
He also appeared to call for the end of protests against his 30-year rule that began on 25 January.

“Egypt has gone through difficult times and we cannot allow it to carry on,” he said.
“The damage to our economy will lead to a situation that the youth calling for reform will be the first to be affected.”
Mr Suleiman, speaking after Mr Mubarak’s address, said the protests had had an effect, and a process of constitutional change would now go ahead.
Egypt’s military had earlier said it was standing ready to “protect the nation”. State news agency Mena reported that the high council of the armed forces was in continuous session “to protect the nation, its gains and the aspirations of the people”.

Negotiations between the government and opposition groups have made little progress, with protesters disillusioned at plans for reform put forward by Mr Mubarak’s government.
The US government had in recent days stepped up its call for the protesters’ concerns to be addressed.