A sense of disintegration in the administration since the protests on Sunday has been heightened by the resignations tendered by several ministers who are not members of Mursi's Muslim Brotherhood. On Tuesday, the state news agency said the foreign minister, Mohamed Kamel Amr, had also asked to step down.
Attacks on Brotherhood offices have added to feelings among Islamists that they are under siege.
Some Brotherhood leaders, who swept a series of votes last year, said they would look to put their own supporters on the streets. After the destruction of the Brotherhood's headquarters in a battle overnight on Monday in which eight people were killed, the possibility of wider violence seems real. World powers are looking on anxiously, including the United States, which has long funded the Egyptian army as a key component in the security of Washington's ally Israel.
(Read More: Egypt Protests Set for Showdown, More Violence Feared)
General Martin Dempsey, the chairman of the Joint Chiefs of Staff, spoke to his Egyptian counterpart, General Abdel Fattah al-Sisi on Monday, although it was unclear what was said.
President Barack Obama has urged Mursi and his rivals to compromise. But Washington has also defended the legitimacy of Mursi's election. It is unclear how far the Egyptian military has informed, or coordinated with, its U.S. sponsors.
The coalition that backed Sunday's protests said there was no question of it negotiating now with Mursi on the general's timetable and it was already formulating its positions for discussion directly with the army once the 48 hours are up.
Sisi, in his broadcast statement, insisted that he had the interests of democracy at heart - a still very flawed democracy that Egyptians have been able to practise as a result of the army pushing aside Hosni Mubarak in the face of a popular uprising.
That enhanced the already high standing of the army among Egyptians, and the sight of military helicopters streaming national flags over Cairo's Tahrir Square at sunset, after Sisi had laid down the law, sent huge crowds into a frenzy of cheers.
(Read More: Egypt Clerics Warns of 'Civil War' as Rallies Begin)
But on the other side of Egypt's polarised politics, a Brotherhood spokesman said it might considering forming "self-defence" committees after a series of attacks on its premises.
Another leading figure in the movement, Mohamed El-Beltagy, said: "The coming period will witness an alignment between all the Islamist forces. Their sons will be called on to demonstrate in all streets and squares of the country."