Crowds gathered to protest against what they say is the rushed drafting of a new constitution, due to be voted on on 15 December.
President Mohammed Morsi was in the palace but left as the crowds outside began to grow, sources there said.
Protesters are also reported to have gathered in large numbers in Egypt’s second city Alexandria.
New powers
Many of those gathered outside the presidential palace chanted slogans similar to those directed against the regime of former president Hosni Mubarak during protests in February 2011.
As well as their complaints about the new constitution, activists have also been angered by a decree issued by Mr Morsi last month in which he awarded himself sweeping powers.
Mr Morsi, elected in Egypt’s first free presidential election in June, says he will give these up once a new constitution is ratified.
On Sunday, tens of thousands of Islamist supporters of Mr Morsi held demonstrations in support of his decisions and of the new constitution.
Source: BBC
Clashes outside Egypt presidential palace in Cairo
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Police have fired tear gas in clashes with tens of thousands of protesters gathered near the presidential palace in the Egyptian capital Cairo. Some of the protesters reportedly cut through barbed wire around the palace.