Egypt's army has denied its ultimatum to feuding politicians to resolve the country's deadly crisis within 48 hours amounts to a coup.
It said earlier it would offer a "road map" for peace if Islamist President Mohammed Morsi and his opponents failed to heed "the will of the people".
Mr Morsi, however, has rejected the ultimatum, saying he will proceed with his own national reconciliation plan.
On Sunday millions rallied nationwide, urging the president to quit.
Meanwhile, Egypt's state news agency Mena reported early on Tuesday that Foreign Minister Mohamed Kamel Amr had submitted his resignation.
If accepted, he would join at least five other ministers who have already reportedly resigned over the political crisis.
Large protests continued on Monday, and eight people died as activists stormed and ransacked the Cairo headquarters of the Muslim Brotherhood, to which the president belongs.
There were reports of gun clashes between rival factions in the city of Suez, east of the capital, on Monday night.
Noisy celebrations erupted in Cairo as protesters interpreted the ultimatum as spelling the end of Mr Morsi's rule.
He became Egypt's first Islamist president on 30 June 2012, after winning an election considered free and fair following the 2011 revolution that toppled Hosni Mubarak.
Coup in the making?
In an announcement read out on Egyptian TV, Gen Abdel Fattah al-Sisi, defence minister and head of the armed forces, described the protests as an "unprecedented" expression of the popular will.
If the people's demands were not met, he said, the military would have to take responsibility for a plan for the future.
But while he said the army would not get involved in politics or government, his words were seen by many as a coup in the making.
However, President Morsi said in a statement early on Tuesday that he was not consulted in advance ahead of the ultimatum announcement.
The presidency "sees that some of the statements in it [the ultimatum] carry meanings that could cause confusion in the complex national environment, it read.
To the sound of blaring car horns and exploding fireworks, tens of thousands of flag-waving supporters of Tamarod (Rebel) - the opposition movement behind the protests - partied in Cairo's Tahrir Square late into the night.
They accuse Mr Morsi of putting the Brotherhood's interests ahead of the country's as a whole.
As five helicopters flew over the square with huge Egyptian flags hanging below them, the crowds chanted: "The army and the people are one hand."
There were similarly jubilant scenes in the Mediterranean city of Port Said and outside Mr Morsi's house in Zagazig, where protesters vowed to continue a sit-in until a clear plan for handing over power was enacted.
Given the inability of politicians from all sides to agree until now, the 48-hour ultimatum makes it unlikely Mr Morsi can survive in power, says the BBC's Aleem Maqbool in Cairo.
But a second statement posted on the military's Facebook page late on Monday emphasised the army "does not aspire to rule and will not overstep its prescribed role".
"Our earlier statement's purpose was to push all parties to find a quick solution to the current crisis... to push towards a national consensus that responds to the people's demands," said the statement.
Senior Brotherhood figure Muhammad al-Biltaji urged pro-Morsi supporters to "call their families in all Egyptian governorates and villages to be prepared to take to the streets and fill squares" to support their president.
"Any coup of any sort will only pass over our dead bodies," he said to a roar from thousands gathered outside the Rab'ah al-Adawiyah mosque in Cairo's Nasr district.
A night-time press conference by the presidency was postponed until Tuesday. Instead, an undated photograph posted on the president's official Facebook page showed Mr Morsi smiling with Gen Sisi and Prime Minister Hisham Qandil.
Obama calls for restraint
The opposition movement had given Mr Morsi until Tuesday afternoon to step down and call fresh presidential elections, or else face a campaign of civil disobedience.
On Saturday, the group said it had collected more than 22 million signatures - more than a quarter of Egypt's population - in support.
And on Monday the ministers of tourism, environment, communication, water utilities and legal affairs reportedly resigned in an act of "solidarity with the people's demand to overthrow the regime".
But Mr Morsi was defiant in an interview published on Sunday, rejecting calls for early presidential elections.
US President Barack Obama has called for restraint on all sides, saying the potential for violence remained.
Although it was not the job of the US to choose Egypt's leaders, it wanted to make sure all voices were heard, said Mr Obama during a visit to Tanzania.