Egypt's political crisis deepened on Tuesday as Islamist President Mohamed Morsi snubbed an army ultimatum threatening to intervene if he did not meet the demands of the people, and five ministers led a spate of government resignations.

The opposition too expressed concern that the military was poised to play a political role in the deeply divided country, even as the army hastened to damp down talk of an imminent "coup.”

An army statement, read out on television Monday, had given Morsi 48 hours to comply with its call, after millions of people took to the streets nationwide to demand the Islamist leader step down. 

"If the demands of the people are not met in this period... (the armed forces) will announce a future roadmap and measures to oversee its implementation," it said.

In a statement issued overnight, the presidency insisted it would continue on its own path towards national reconciliation.

The army declaration had not been cleared by the presidency and could cause confusion, it said.

The presidency also denounced any declaration that would "deepen division" and "threaten the social peace.”

The president was consulting "with all national forces to secure the path of democratic change and the protection of the popular will", it added.

In Cairo, both Morsi supporters and opponents prepared for mass demonstrations later on Tuesday.

Backers of the president joined a sit-in in his support in Cairo's Nasr City neighborhood, as hundreds more gathered near Cairo University vowing to defend his legitimacy.

In Tahrir Square, the jubilant mood following the army's statement gave way to tension, with fears of violence in the coming days.

"The regime is no longer legitimate," said Mostafa Gharib, adding that he feared the Islamists would "fight to the end" nonetheless.

Accountant Mona Elghazawy said she was "very worried.” "It's now a battle between all the state institutions and the Islamists."

In Cairo, most businesses remained closed and very few cars were on the streets, highlighting the anxiety on what would normally have been a busy working day.

Morsi's supporters say any attempt to remove Egypt's first freely elected president from power is no less than a coup.

Egypt's main opposition coalition, the National Salvation Front, said it would "not support a military coup."

It expressed trust in the army's insistence that it does not want to get involved in politics.

The army denied there was any attempt at a "coup", saying that army chief Abdel Fattah al-Sisi's statement was merely aimed at "pushing all political sides to quickly find a solution."

As the political uncertainty grew, Morsi was hit with a spate of resignations, including by his foreign minister Mohammed Kamel Amr and the ministers of tourism, environment, investment and legal affairs.

Presidential spokesman Ehab Fahmy and cabinet spokesman Alaa al-Hadidi also resigned, officials and the media reported.

Adding to Morsi's woes, an Egyptian court on Tuesday ordered the reinstatement of Abdel Meguid Mahmud, the public prosecutor he had sacked in November.

US President Barack Obama, whose government is a major military aid donor to Egypt, called Morsi to warn him that the voices of all Egyptians must be heard, a White House official said.

Obama placed the call from Tanzania, the final stop of an African tour, and told him Washington was committed to "the democratic process in Egypt and does not support any single party or group," the official said.

A longtime leader of the long banned if normally tolerated Muslim Brotherhood, Morsi was catapulted to power by the 2011 uprising that ended three decades of Hosni Mubarak's authoritarian rule.

Monday's statement from the army came a day after millions of protesters took to the streets across Egypt demanding Morsi's resignation, dwarfing counter-demonstrations in his support.

It received a rapturous welcome from Morsi's opponents, who spilled onto the streets in Cairo, Alexandria and other big cities, waving flags and chanting support for the army.

Tamarod, the grassroots campaign behind Sunday's massive protests, also hailed the statement saying the army had "sided with the people.”

It "will mean early presidential elections", Tamarod spokesman Mahmud Badr told reporters.

The movement had issued its own ultimatum to Morsi, giving him until 5:00 pm (1500 GMT) on Tuesday to quit or face an open-ended campaign of civil disobedience.

Sixteen people died in Sunday's protests, including eight in clashes between supporters and opponents of the president outside the Cairo headquarters of the Muslim Brotherhood.

Early on Monday, protesters set the Brotherhood's headquarters ablaze before looting it.

Morsi's opponents accuse him of having betrayed the revolution by concentrating power in Islamist hands and of sending the economy into freefall.

His supporters say he inherited many problems from a corrupt regime, and that he should be allowed to complete his term, which runs until 2016. (AFP)