In the capital here, thousands of people massed at the iconic Tahrir Square - the epicentre of pro-democracy protests in 2011 - under the banner of Tamarod (Rebellion) movement which is driving the campaign with a petition of signatures seeking 61-year-old Morsi's ouster and a snap election.
Anti-government protesters also stormed the national headquarters of Muslim Brotherhood here. They also ransacked the six-storey building and set it on fire.
"We give Mohamed Morsi until 5:00 pm (1500 GMT) on Tuesday July 2 to leave power, allowing state institutions to prepare for early presidential elections," Tamarod said in a statement on its website.
The statement warned that Morsi would face a campaign of civil disobedience if he did not leave power by tomorrow.
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Opposition activists claim more than 22 million people in the nation of 84 million have signed the petition and have urged the signatories to come out in Tahrir Square.
One each died in the provinces of Fayoum, Beni Sueif and Kafr el-Sheikh. One protester died during a rally outside the presidential palace and another died in Alexandria, the ministry said.
Thousands of ordinary Egyptians - angered by Morsi's policies - also took part in the rallies, described as the biggest protest in the history of Egypt.
The crowds seen in the Tahrir Square were the biggest since the 2011 revolution that ousted long time ruler Hosni Mubarak.