President Hosni Mubarak has defended the role of Egypt's security forces in suppressing anti-government protests which have rocked the country.
Mr Mubarak also dismissed his government and said a new cabinet would be announced on Saturday.
It was his first statement since the protests - in which at least 26 have died with hundreds injured - began.
Tens of thousands took part in protests in Cairo, Suez, Alexandria and other cities.
Protesters set fire to the headquarters of the governing NDP party and besieged state TV and the foreign ministry.
At least 13 people were killed in Suez on Friday, while in Cairo, five people died, according to medical sources.
That brings the death toll to at least 26 since the protests began on Tuesday.
"I have asked the government to present its resignation today," Mr Mubarak said, adding that he would appoint a new government on Saturday.
He also said he understood the protesters' grievances but that a thin line divided liberty from chaos and he would not allow Egypt to be destabilised.
One protester told the Associated Press news agency: "We want Mubarak to go and instead he is digging in further."
In a televised address shortly after Mr Mubarak spoke, US President Barack Obama said he had spoken at length with the Egyptian president and urged him to turn "a moment of volatility" into "a moment of promise".
The BBC's Jon Leyne in Cairo says there had clearly been a lot of discussion behind the scenes before Mr Mubarak spoke to the country.
But his comments will probably just provoke further unrest, says our correspondent - the people on the streets will be infuriated by his accusations that they are seeking to destabilise the country; they will also be inspired by the belief that, having wrung some concessions from him, they could yet oust him.
After Mr Mubarak spoke, a sustained volley was heard from central Cairo, which our correspondent said could have been either tear gas or live fire.
The Reuters news agency later quoted witnesses as saying more than 20 military vehicles rolled in to central Tahrir Square shortly after midnight, scattering protesters into the sidestreets.
The BBC's Rupert Wingfield-Hayes, in Suez, says the streets of the port city were left to the protesters overnight but the army has now arrived there.
After days of unrest, protests erupted again on Friday, as tens of thousands of protesters across the country turned out after Friday prayers shouting "Down, down with Mubarak" and, "The people want the regime to fall".
The authorities announced a curfew from 1800 to 0700 local time (1600-0500 GMT), but it was immediately and widely flouted.
At several locations, riot police responded by firing rubber bullets and tear gas, and by using water cannon.
The headquarters of the governing NDP party was set ablaze, while protesters also besieged the state broadcaster and the foreign ministry.
The army secured the Egyptian Museum, next door to the NDP building and home to such treasures as the gold mask of King Tutankhamen, to protect it from looters.
Internet and phone services - both mobile and land-line - have been severely disrupted, although protesters are using proxies to work around the restrictions.
The BBC said it would forcefully protest to the Egyptian authorities after a reporter for BBC Arabic, Assad Sawyer, arrested and beaten by plainclothes policemen in Cairo.
Mr Obama said he had told Mr Mubarak to respect the rights of the Egyptian people and refrain from using violence against peaceful protesters - but he said the protesters also had a responsibility to express themselves peacefully.
He urged the Egyptian leader to take "concrete steps that advance the rights of the Egyptian people" and deliver on the promises of reform in his address.
"Violence will not address the grievances of the Egyptian people. And suppressing ideas never succeeds in making them go away," he said.
"Surely, there will be difficult days to come, but the United States will continue to stand up for the rights of the Egyptian people and work with their government in pursuit of a future that is more just, more free and more hopeful."
The BBC's Paul Adams in Washington said there is no immediate suggestion that the White House is cutting its ties with its long-time ally Mr Mubarak.
But it is clearly giving him the chance to turn the unrest into what Mr Obama described as "a moment of promise", says our correspondent.
Earlier, White House spokesman Robert Gibbs said Washington would review its aid to Egypt based on events in the coming days.
Egypt is the fourth largest recipient of American aid, after Afghanistan, Pakistan and Israel.
Britain, the US and France are all advising against non-essential travel to Egypt.
The unrest follows an uprising in Tunisia two weeks ago, in which President Zine al-Abidine Ben Ali was toppled after 23 years in power.
The Tunisian upheaval began with anger over rising food prices, high unemployment and anger at official corruption - problems which also left many people Egypt feeling frustrated and resentful of their leadership.