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 the details of this remain unclear.
Thousands of anti-government protesters in Cairo's Tahrir Square reacted angrily to his announcement.
There were chants of "Down with Mubarak", and protesters waved their shoes in disgust. Thousands were reported to be heading towards the presidential palace some distance away.
The BBC's Paul Adams, in Tahrir Square, said the mood contrasted dramatically with the celebratory, almost party atmosphere that existed in the hours running up to President Mubarak's televised address.
Mr Mubarak had previously pledged not to stand in September's poll, and said he would stay on to oversee a process of constitutional change.
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 Egyptian ambassador to the US, Sameh Shoukry, suggested Vice President Suleiman was now the "de facto head of state" following Mr Mubarak's speech, but this has not been confirmed.
In his address, Mr Mubarak said: "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."
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.
Mr Mubarak added that the country's emergency laws would only be lifted when conditions were right, and said he would ignore "diktats from abroad".
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 these to carry on," he said. "The damage to our economy will lead to a situation in which 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.
He added that President Mubarak had empowered him to preserve security and stability in Egypt, and restore normality - and he urged the protesters to return home.
"Youth of Egypt: go back home, back to work, the nation needs you to develop, to create. Don't listen to radio and TV, whose aim is to tarnish Egypt," he said.
Activist Mustafa Naggar, responding to the leadership's statements, said: "The street is fed up with Mubarak. If Mubarak leaves the country, he will help to calm the crisis. If he continues, he will lead Egyptians into chaos.
"Plans for tomorrow stand. We will march in the millions to Tahrir Square and other locations."
Leading opposition figure Mohamed ElBaradei, a former head of the United Nations atomic watchdog, tweeted: "Egypt will explode. Army must save the country now."
Among the first reaction from the US - a key ally of Egypt - was a statement from Senator John McCain, in which he described President Mubarak's announcement that he will remain in power as "deeply unfortunate and troubling".
He added: "The voices of the Egyptian people are growing louder and more unified, and they are not demanding partial transfers of power or minor adjustments to the current government."
US President Barack Obama has convened a meeting with his national security team at the White House following President Mubarak's speech. The US government had in recent days stepped up its call for the protesters' concerns to be addressed.
The European Union's chief diplomat, Baroness Ashton, said: "The time for change is now. President Mubarak has not yet opened the way to faster and deeper reforms.
"We will pay close attention to the response by the Egyptian people in the coming hours and days."
Earlier, the secretary-general of the Mr Mubarak's ruling National Democratic Party, Hossam Badrawi, had said the right thing for the president to do would be to step aside - and that he did not expect Mr Mubarak to be president on Friday.
At the same time, Egypt's military announced 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".