Many Egyptians are dissatisfied with the leadership of the Muslim Brotherhood.
Waving Egyptian flags and carrying posters of Morsi crossed out in red, crowds packed central Cairo's Tahrir square, the birthplace of the 2011 uprising against autocrat Hosni Mubarak, and chanted "erhal!", or "leave!"
"Today is the Brotherhood's last day in power," said Suliman Mohammed, a manager of a seafood company who was protesting at Tahrir. "I came here today because Morsi did not accomplish any of the (2011) revolution's goals. I don't need anything for myself, but the needs of the poor were not met."
A tidal wave of opponents also marched on the Ittihadiya presidential palace. The crowds, including women, children and elderly people, hoisted long banners in the colors of the Egyptian flag and raised red cards - a sign of expulsion in soccer.
At the same time, thousands of Islamists gathered outside the Rabia al-Adawiya Mosque in a show of support for Morsi.
"The people hold the legitimacy and we support Dr. Mohamed Morsi," Ahmed Ramadan, one of those at the rally near the mosque said. "We would like to tell him not to be affected by the opponents' protests and not to give up his rights we are here to support and protect him."
The demonstrations are the culmination of polarization and instability that have been building since Morsi's inauguration as Egypt's first freely elected leader on June 30, 2012.
The youth activist group known as Tamarod, Arabic for "Rebel," announced Saturday that more than 22 million people had signed a petition calling for Morsi to step down. Morsi's supporters have questioned the authenticity and validity of the signatures, but have produced no evidence of fraud.
Morsi has three years left on his term. He has said he will not step down, saying street protests cannot be used to overturn the results of a free election.
"There is no room for any talk against this constitutional legitimacy," Morsi told Britain's The Guardian newspaper in an interview published Sunday, rejecting early elections.
If an elected president is forced out, "well, there will (be) people or opponents opposing the new president too, and a week or a month later, they will ask him to step down," he said.
Already at least seven people, including an American, have been killed in the protests this past week. The State Department says 21-year-old Andrew Pochter from Chevy Chase, Md., was killed while taking photos of the violent clashes. Pochter was a student at Kenyon College in Gambier, Ohio, and was working in Egypt as an intern for AMIDEAST, a non-profit education organization.
The Associated Press contributed to this report.