Some protesters have said they won't leave until Morsi rescinds a decree he issued last month granting him broad powers and exempting his actions from judicial review, Voice of America reported.
Riot police Tuesday lobbed tear gas outside the presidential palace where tens of thousands of protesters gathered while Morsi was inside. After trying to stop the demonstrators from storming the palace, police retreated and allowed marchers through a barrier and up to the palace walls.
Egyptian officials said Morsi left the palace.
Egypt Independent said photos broadcast on state television Wednesday showed protesters setting up tents. State news agency MENA said 24 tents were in place outside the palace.
Many marchers shouted anti-government slogans similar to ones used during the uprising last year that ousted former President Hosni Mubarak.
Protest leaders said Tuesday's march was a final warning to Morsi to step away from his decree, Voice of America said. The demonstrators also are against a draft constitution opposition leaders said was drawn up by Islamists who ignored input from secularists and liberals.
A referendum on the constitution will be Dec. 15.
Also Tuesday, 11 Egyptian newspapers suspended publication to protest the draft constitution, which journalists said restricts free speech, Voice of America said.
The Constitution Party said it would conduct a sit-in at the palace until Friday, the Independent said. The party also called for marches and support for a comparable demonstration in Tahrir Square.