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.
"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.
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.
Meanwhile, reports said seven people have been killed and hundreds injured in sporadic outbreaks of violence, raising fears of an escalation in violence in the country.
Also Read
Five people were shot in Nile Valley towns south of Cairo and two were killed in violence outside the Muslim Brotherhood's headquarters in the capital late yesterday on the first anniversary of Morsi's election as the president.
Thousands spent the night at Tahrir Square, focus of the Arab Spring protests which brought down Hosni Mubarak regime.
Morsi's opponents say he has failed to tackle economic and security problems. Critics also say he has put the Islamist agenda of his Muslim Brotherhood party ahead of the country's wider interests.
In Cairo, anti-Morsi supporters waving red cards chanted: "Irhal! Irhal!" ("Leave! Leave!"). Similar rallies were held in Alexandria, Kafr al-Sheikh, Sidi Salem, Damietta, Gharbiya, Suez, Sharqiya - the birthplace of Morsi, and other cities.
Muslim Brotherhood's political wing, the Freedom and Justice Party, also vowed the pro-Morsi coalition will remain in sit-ins to defend until opposition end their rallies.
Egyptian presidency urged all political forces to commit to peaceful protest, insisting 'dialogue' is only way out of impasse. "Dialogue is the only way to reach consensus," said a presidential spokesman yesterday.