Thousands pressed against the palace gates amid thunderous chants of "We won't leave! He should leave!" Some climbed atop the military vehicles that ringed the complex and spray-painted anti-Islamist slogans on the walls.
Protesters clashed sporadically with security forces using tear gas outside the palace and near Tahrir Square on Tuesday night. Witnesses said that some of the riot police appeared to join the crowd, underscoring what they said was opposition to Morsi within his security services.
Morsi did not comment on the unrest but left the presidential compound during the protest, the Reuters news agency reported.
The Islamists and their opponents have described Egypt's deepening crisis, which centers on a draft of the new constitution, as a battle for the country's soul and the success of its faltering transition to democracy.
Morsi set a date of Dec. 15 for a national referendum on the draft after the Islamist-dominated assembly tasked with writing it rushed to approve it last week, deepening the political rift over his decree and leaving the opposition divided over what to do if the referendum is carried out.
Opposition to the decree by senior justice officials had threatened to undermine the administration's ability to hold a referendum on the document. On Monday, however, the Supreme Judicial Council agreed to oversee the process, clearing the way for the Dec. 15 vote and creating the possibility of legal credibility for the results.
Even as protesters kept up their demands and a handful of independent news organizations began a symbolic media blackout to show their objection to the draft, opposition leaders remained divided Tuesday on whether to boycott the referendum or simply vote no.