Mubarak addressed his remarks to the "youth of Egypt in Tahrir Square"Egypt's President Hosni Mubarak has said he will stay in office and transfer all power only after September's presidential election.
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.
"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 law would only be lifted when conditions were right.
Egypt's military had earlier said it was standing ready to "protect the nation".
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.
