Egypt's president Hosni Mubarak has appeared on national television, saying he intends to work in his remaining months as president to ensure a smooth transfer of power.
In the late-night address, Mr Mubarak said he would not stand for re-election in September and called on the government to ensure political, social and economic reform.
Hundreds of thousands of people had massed in Cairo and other Egyptian cities to demand that President Mubarak leave power after a 30-year rule.
In the centre of Cairo, Tahrir Square was jammed with people and crowds also demonstrated in Alexandria, Suez and in the Nile Delta.
In his address, Mr Mubarak criticised the protests, saying what began as a civilised phenomenon turned into a violent event controlled by cowards. He said he had offered to meet all parties but some had refused dialogue.
Mr Mubarak ended his speech by saying that he would not leave Egypt, the BBC reports.
One of the protest leaders, Mohamed ElBaradei, says Mr Mubarak must resign in order to spare bloodshed and must leave Egypt in order for dialogue to begin.
He told an Arabic television network that comprehensive discussions are needed on the shape of a post-Mubarak Egypt.
Meanwhile, the United Nations says as many as 300 people may have died during the past week of anti-government unrest.
UN Human Rights Commissioner Navi Pillay says the exact number is unconfirmed, but she is alarmed at the casualty toll from clashes between demonstrators and police on Friday.
In other developments:
The head of the US Senate Committee on Foreign Relations, John Kerry, has called for Mr Mubarak to recognise that it is time to leave office.
The US ambassador to Egypt is reported to have had a telephone conversation with opposition figure Mohamed ElBaradei.
The Australian Government has organised a second Qantas emergency flight to help its citizens leave Egypt after 400 people registered for the first one.
Britain's government has chartered another aircraft to step up the evacuation of UK nationals.