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. – Bbcnews