The military's statement puts enormous pressure on Morsi and his Muslim Brotherhood. So far, the president has vowed he will remain in his position, but the opposition and crowds in the street who numbered in the millions nationwide on Sunday have made clear they will accept nothing less than his departure and a transition to early presidential elections.
That makes action by the generals when the deadline runs out nearly inevitable, since a deal seems unlikely. The statement did not define the "people's demands" that must be met. But it strongly suggested that Sunday's gigantic rallies expressed the desire of Egyptians, raising the likelihood it would insist on Morsi's departure.
An army move against Morsi, however, risks a backlash from his Islamist supporters, who include hard-line former militants.
Morsi met Monday with el-Sissi and Prime Minister Hesham Kandil, according to the president's Facebook page, without giving further details.
Already, the military's presence in Cairo has increased at sensitive spots the past two days. Troops on Monday manned checkpoints on roads leading to a pro-Morsi rally of Islamists near his palace. They checked cars for weapons, after repeated reports some Islamists were arming themselves.
Morsi's backers have been infuriated by what they call an opposition move to forcibly overthrow Egypt's first president chosen in a democratic election. Some see the campaign as aimed at defeating the "Islamist project."
In the evening, the pro-president rally outside the Rabia al-Adawiya Mosque not far from the Ittihadiya palace also swelled, though it was eclipsed by the opposition rallies. Its participants blew whistles and waved banners with Morsi's picture on it.
"The military has sacrificed legitimacy. There will be a civil war," Manal Shouib, a 47-year-old physiotherapist at the pro-president rally outside the Rabia al-Adawiya Mosque not far from Ittihadiya.
Mohammed Saeed, another Morsi supporter, vowed that he would fight the military if the president is ousted.
"If he (el-Sissi) wants to get rid of us, we will not run. We will face bullets with our bodies. Let the general commander of the armed forces respect his president."
The sense of predicament among Morsi's supporters was apparent as they concluded the sunset prayers with a supplication.
"May God answer the prayers of these extended hands to You. God, accept us as martyrs for Your cause and make Your slave Mohammed Morsi victorious," said the imam who led the prayers. Muslims routinely refer to themselves as slaves of God.
In a sign of Morsi's growing isolation, five Cabinet ministers said on Monday they have resigned their posts to join the protest movement, the state news agency said. The five are the ministers of communications, legal affairs, environment, tourism and water utilities, MENA reported.
The governor of the strategic province of Ismailia on the Suez Canal, Hassan el-Rifaai, also quit Monday, saying he made the decision in the interest of the nation.
Monday's statement was the military's second ultimatum. Earlier, el-Sissi gave the two sides a week to reach an agreement. That ultimatum expired on Sunday, with Morsi repeating his longstanding offer for dialogue, which the opposition rejected.
On Monday, the military praised the anti-Morsi protests as "glorious," saying the participants expressed their opinion "in peaceful and civilized manner," and that "it is necessary that the people get a reply ... to their calls."
The military underlined it will "not be a party in politics or rule." But it said it has a responsibility to act because Egypt's national security is facing a "grave danger," according to the statement.
It said it repeats its call "for the people's demands to be met," giving all sides 48 hours "as a last chance to shoulder the burden of the historic moment."
If the demands are not realized in that time, the military would be obliged to "announce a road-map for the future and the steps for overseeing its implementation, with participation of all patriotic and sincere parties and movements ... excluding no one."
The group that organized Sunday's mass rallies, Tamarod, issued an ultimatum of its own earlier Monday, giving Morsi until the next day at 5 p.m. (1300 GMT) to step down or it would escalate its campaign with larger marches and "complete civil disobedience."
It also urged the military and police to make clear their support for the protesters. When the military statement came out hours later, it made no changes in its own ultimatum.
The swiftness of the military's new statement suggested it was prompted by the stunning turnout by the opposition on Sunday and the eruptions of violence that point to how the confrontation could spiral into chaos if it continues.
Sunday's protests were the largest seen in Egypt in the 2½ years of turmoil since the ouster of autocrat Hosni Mubarak in February 2011. Millions packed Cairo's Tahrir Square, the streets outside the Ittihadiya presidential palace and main squares in cities around the country on the anniversary of Morsi's inauguration.
The main rallies in Cairo were largely peaceful, but deadly violence broke out in several parts of the country, often when marchers came under gunfire, apparently from Islamists.
At least 16 people were killed and more than 780 injured, Health Ministry spokesman Yehya Moussa told state television.
In Cairo, protesters Sunday night attacked the Brotherhood's main headquarters, pelting it with stones and firebombs. Brotherhood backers barricaded inside opened fire on them in clashes that went on for hours and left eight dead. In the early hours Monday, protesters breached the walls of the six-story luxury villa and stormed inside.
They carted off furniture, files, rugs, blankets, air conditioning units and portraits of Morsi, according to an Associated Press journalist at the scene. One protester emerged with a pistol and handed it over to a policeman outside.
Footage on local TV networks showed smashed windows, blackened walls and smoke billowing out of the fortified villa in the Muqattam district in eastern Cairo. A fire was still raging on one floor hours after the building was stormed. One protester tore down the Muslim Brotherhood sign from the building's front wall, while another hoisted Egypt's red, black and white flag out an upper-story window and waved it in the air in triumph.
Morsi's critics view the Brotherhood headquarters as the seat of real power in Egypt, consistently claiming that the Islamist group's spiritual leader, Mohammed Badie and his powerful deputy, Khairat el-Shater, actually call the shots behind Morsi. Morsi and Brotherhood officials have denied this and say they have tried to give opponents a greater voice, only to be spurned.
On Monday, the anti-Morsi brought their rallies into a second day.
Some protesters spent the night in dozens of tents pitched in the capital's central Tahrir Square and in front of the president's Ittihadiya Palace.
The anti-Morsi demonstrators are calling for widespread labor strikes in an attempt to ratchet up the pressure on the president, but it was not immediately clear whether unions would respond to the call. Organizers are also calling for sit-ins at the Cabinet building, interim parliament, and another presidential place where Morsi has been working since late last week instead of Ittihadiya.
The military has for months been sending subtle but telling messages that it was not pleased with the policies pursued by Morsi and his Brotherhood.
Morsi was clearly scolding el-Sissi when he said in a televised address last Wednesday that the armed forces should focus on improving its capabilities.
The military seemed to reject that in its statement Monday, underlining that it "is a main player in the nation's future" and has "a national and historic duty to protect the security and safety of the nation."
Morsi has said he will not quit, saying that street action must not be allowed to remove an elected president or else the same could happen to future presidents.
For weeks, Morsi's supporters have depicted the planned protest as a plot by Mubarak loyalists to return to power. But their claims were undermined by the extent of Sunday's rallies. In Cairo and a string of cities in the Nile Delta and on the Mediterranean coast, the protests topped even the biggest protests of the 2011's 18-day uprising, including the day Mubarak quit, Feb. 11, when giant crowds marched on Ittihadiya.
The mood was largely festive at Sunday's giant anti-Morsi rallies in Tahrir and outside the Ittihadiya palace.
Fireworks went off overhead. Men and women, some with small children on their shoulders, beat drums, danced and sang, "By hook or by crook, we will bring Morsi down." Residents in nearby homes showered water on marchers below some carrying tents in preparation to camp outside the palace to cool them in the summer heat, and blew whistles and waved flags in support.
"Mubarak took only 18 days although he had behind him the security, intelligence and a large sector of Egyptians," said Amr Tawfeeq, an oil company employee marching toward Ittihadiya with a Christian friend. Morsi "won't take long. We want him out and we are ready to pay the price."
Associated Press writers Maggie Michael and Mariam Rizk contributed to this report. Text of Egyptian military ultimatum
The text of the Egyptian military statement issued Monday warning the armed forces will intervene if the demands of the people aren't met in 48 hours.
"Egypt and the whole world witnessed yesterday demonstrations by the great people of Egypt expressing their opinion in an unprecedented, peaceful and civilized way.
Everyone saw the movement of the Egyptian people and heard their voices with the greatest respect and concern. It is necessary that the people receive a reply to their movement and the call from every party with any responsibility in the dangerous circumstances surrounding the nation.
As a main party in the considerations of the future and based on their patriotic and historic responsibilities to protect security and stability, the Armed Forces state the following:
The Armed Forces will not be a party in the circles of politics or governance and are not willing to step out of the role defined for them by the basic ideals of democracy based on the will of the people.
The national security of the state is exposed to extreme danger by the developments the nation is witnessing, and this places a responsibility on us, each according to his position, to act as is proper to avert these dangers. The armed forces sensed early on the dangers of the current situation and the demands the great people have at this time. Therefore, it previously set a deadline of a week for all political forces in the country to come to a consensus and get out of this crisis. However, the week has passed without any sign of an initiative. This is what led to the people coming out with determination and resolve, in their full freedom, in this glorious way, which inspired surprise, respect and attention at the domestic, regional and international levels.
Wasting more time will only bring more division and conflict, which we have warned about and continue to warn about. The noble people have suffered and have found no one to treat them with kindness or sympathize with them. That puts a moral and psychological burden on the armed forces, which find it obligatory that everyone drop everything and embrace these proud people, which have shown they are ready to do the impossible if only they feels there is loyalty and dedication to them.
The Armed Forces repeat their call for the people's demands to be met and give everyone 48 hours as a last chance to shoulder the burden of the historic moment that is happening in the nation, which will not forgive or tolerate any party that is lax in shouldering its responsibility.
The Armed Forces put everyone on notice that if the demands of the people are not realized in the given time period, it will be obliged by its patriotic and historic responsibilities and by its respect for the demands of the great Egyptian people to announce a road map for the future and the steps for overseeing its implementation, with participation of all patriotic and sincere parties and movements including the youth, who set off the glorious revolution and continue to do so without excluding anyone.
A salute of appreciation and pride to the sincere and loyal men of the Armed Forces, who have always borne and will continue to bear their patriotic responsibilities toward the great people of Egypt with determination, decisiveness and pride.
God save Egypt and its proud, great people."