Otherwise, “Tuesday, 5:00 pm will be the beginning of a complete civil disobedience campaign.”
The health ministry said 16 people died in nationwide protests, including eight in clashes between supporters and opponents of Morsi outside the Cairo headquarters of the Muslim Brotherhood movement from which he hails.
Another three people died in the central province of Assiut and one each in Fayoum, Beni Sueif and Kafr el-Sheikh provinces.
One protester suffocated to death at a rally outside the presidential palace in Cairo and another died of wounds in the coastal city of Alexandria, the ministry said.
Early on Monday, protesters set the Brotherhood’s headquarters ablaze before storming it and ransacking it, an AFP correspondent reported.
Looters left with petrol bombs, helmets, flak jackets, furniture, televisions and documents.
“This is a historic moment. The Brotherhood ruined the country, so stealing from them is justified,” one told AFP.
A senior government official told AFP that four ministers — tourism, environment, communication and legal affairs — had tendered their resignations to Prime Minister Hisham Qandil.
Tourism minister Hisham Zazou had already tried to resign last month after Morsi appointed Adel al-Khayat, a member of an Islamist party linked to a massacre of tourists in Luxor, as governor of the temple city.
Monday’s resignations were a further blow to Morsi, who since coming to power has battled with the judiciary, the media and the police.
Tamarod — Arabic for rebellion — is a grassroots campaign which says it collected more than 22 million signatures to a petition declaring a lack of confidence in Morsi.
It was behind Sunday’s protests that saw millions of people demand his departure on the first anniversary of his inauguration.
As Morsi stood firm and insisted the only way forward was dialogue, calls for army intervention increased.
Tamarod urged state institutions to support the protesters, calling on “the army, the police and the judiciary to clearly side with the popular will as represented by the crowds”.
Opposition leader Hamdeen Sabbahi urged military intervention if Morsi refused to quit.
The army, which led a tumultuous transition after Mubarak’s ouster, had already warned it would intervene if there was major unrest.
“The armed forces must act, because they have always been on the side of the people” which “has expressed its will”, said Sabbahi, who came third in last year’s presidential election.
The best outcome would be for Morsi to go willingly, he added.
But Morsi’s spokesman Ehab Fahmy told reporters: “Dialogue is the only way through which we can reach an understanding… The presidency is open to a real and serious national dialogue.”
Overnight, as protesters pelted the Muslim Brotherhood building in Cairo with petrol bombs, Brotherhood supporters responded with birdshot.
An AFP journalist also reported automatic weapons fire.
In Tahrir Square, where hundreds of protesters spent the night, demonstrators blew whistles and chanted anti-Morsi slogans.
Outside the presidential palace, hundreds more staged a sit-in after the army estimated that millions had heeded the opposition call to protest.
Sunday’s turnout was described as the largest protest in Egyptian history.
“Long live the people,” read Monday’s headline in the independent daily Al-Tahrir, while Al-Masry al-Youm called it the “June 30 revolution”.
Anti-Morsi protests were held in Alexandria, the Nile Delta cities of Mansura, Menuf, Tanta and Mahalla, the canal cities of Suez and Port Said and the president’s hometown Zagazig.
In Tahrir Square, protesters brandished red cards and Egyptian flags as patriotic songs played.
“The people want the ouster of the regime,” they chanted, echoing the signature slogan of the 2011 revolt that ousted Hosni Mubarak and eventually brought Morsi to power.
His supporters have staged counter rallies and there had been fears of major confrontations.
But Sunday’s anti-government protests eclipsed the loyalists’ gathering in Cairo’s Nasr City neighbourhood, which the army estimated attracted some 25,000 people.
Police and troops had deployed at key buildings nationwide, including at vital Suez Canal installations.
Hospitals also went on high alert as banks and most offices closed.
Last week, eight people including an American were killed and scores were injured as rivals clashed.
Morsi, previously a senior Brotherhood leader, is Egypt’s first freely elected president, catapulted to power by the uprising that ended three decades of Mubarak rule.
His opponents accuse him of betraying the revolution by concentrating power in Islamist hands and of sending the economy into freefall.
Morsi supporters say he inherited many problems from a corrupt regime, and that he should be allowed to complete his term which ends in 2016.
Any attempt to remove him would be a coup, they say.
Opponents insist calls for his resignation are aimed at restoring the revolution’s cornerstones of democracy, freedom and social justice.