Those statements, along with the damage to Egypt's economy, appeared to weaken Mr. Mubarak's grip on power just two weeks after a group of young political organizers called on Facebook for a day of protest inspired by the ouster of another Arab strongman, in Tunisia.
Hundreds of thousands have turned out into the streets over the last six days, and organizers called on millions of Egyptians to protest on Tuesday.
Within hours on Monday, the political landscape of the country shifted as decisively as it had at any moment in Mr. Mubarak's three decades in power. The military seemed to aggressively assert itself as an arbiter between two irreconcilable forces: a popular uprising demanding Mr. Mubarak's fall and his tenacious refusal to relinquish power.
How far Mr. Mubarak is offering to bend in negotiations remains to be seen, and given the potential ambiguities of both statements it is too soon to write off the survival of his government.
But the six-day-old uprising here entered a new stage about 9 p.m. when a uniformed military spokesman declared on state television that "the armed forces will not resort to use of force against our great people." Addressing the throngs who took to the streets, he declared that the military understood "the legitimacy of your demands" and "affirms that freedom of expression through peaceful means is guaranteed to everybody."
A roar of celebration rose up immediately from the crowd of thousands of protesters still lingering in Tahrir Square, where a television displayed the news. Opposition leaders argued that the phrase "the legitimacy of your demands" could only refer to the protests' central request -- Mr. Mubarak's departure to make way for free elections.
About an hour later, Omar Suleiman, Mr. Mubarak's right-hand man and newly named vice president, delivered another address, lasting just two minutes.
"I was assigned by the president today to contact all the political forces to start a dialogue about all the raised issues concerning constitutional and legislative reform," he said, "and to find a way to clearly identify the proposed amendments and specific timings for implementing them."
The protesters in the streets took Mr. Suleiman's speech as essentially a capitulation to the army's refusal to use force against them. "The army and the people want the collapse of the government," they chanted in celebration.
Even some supporters of Mr. Mubarak acknowledged that events may have turned decisively against him once the military indicated its support for the protesters, especially given the historical independence of the Egyptian military.
"The army is not a puppet in the hands of anybody," said Mahmoud Shokry, a former Egyptian diplomat and a friend of Mr. Suleiman. "It is not a puppet in the hands of Mubarak. It is not a puppet in the hands of Omar Suleiman. It is not a puppet in the hands of the defence secretary."
"The army does not want to confront the youth," Mr. Shokry said. "If they think this will make a kind of civil war, they will ask Mr. Mubarak to leave the country, I am sure."
Mr. Mubarak's previously unquestioned authority had already eroded deeply over the preceding three days. On Friday, hundreds of thousands of unarmed civilian protesters routed his government's heavily armed security police in a day of street battles, burning his ruling party's headquarters to the ground as the police fled the capital. On Saturday, Mr. Mubarak deployed the military in their place, only to find the rank-and-file soldiers fraternizing with the protesters and revolutionary slogans being scrawled on their tanks.
And on Sunday, leaders of various opposition groups met to select Mohamed ElBaradei, the Nobel Prize-winning former director of the International Atomic Energy Agency, to negotiate for them in anticipation of talks with Mr. Mubarak about forming a transitional unity government -- an idea Mr. Mubarak's surrogate embraced Monday.
Mr. Mubarak's government came under pressure from another front as well: the swift deterioration of the economy. The protests, and the spectre of looting that followed the police withdrawal, have devastated tourism, the source of half of Egypt's foreign income, and shut down transportation.
Ragui Assaad, an economist at the University of Minnesota, said the potential collapse of the economy was like a gun to Mr. Mubarak's head. "If it's a complete shutdown like this, and it lasts for a few weeks, that is going to be really serious," he said.
On Monday foreign embassies scrambled to book charter flights to evacuate their citizens as thousands of people jammed the Cairo airport trying to flee the country. International companies, including those in the vital oil and natural gas industries, shuttered their operations.
As late as midday, however, Mr. Mubarak seemed to be trying to wait out the protesters. He appeared on television soberly shaking the hands of a new roster of cabinet ministers in a public demonstration that even though protesters may control the streets, he remained head of state.
He reinstated about half of the cabinet he had dismissed three days ago in a bid to soothe the unrest. Indeed, in a sign that he may be digging in for a prolonged battle, he added the position of deputy prime minister to the duties of his powerful defence minister, Mohammed Tantawi, who will serve under Ahmed Shafiq, a former air force commander he had appointed as prime minister.
The most notable cabinet change was in the official in charge of suppressing the protests. Mr. Mubarak replaced Interior Minister Habib el-Adly, criticized by human rights advocates for tolerating torture and other police abuses and widely reviled here. He was succeeded by Mahmoud Wagdy, a retired general who had been the head of the Cairo criminal investigations division and a former head of prisons.
The street protests were gearing up again, but with a notably different face. For the first time the Muslim Brotherhood stepped to the fore as the protest organizers called their most reliable foot soldiers as reinforcements.
Though outlawed here because of its Islamist ideology, the Brotherhood is the only group in Egypt able to call out a large and disciplined network of experienced organizers, and their presence on Monday was unmistakable.
Most of the week's protests appeared to represent a nearly universal cross section of the public, coming together spontaneously with little leadership or direction. But as hundreds poured out of midday prayers at a mosque in the neighbourhood of Mohandeseen and marched toward Tahrir Square on Monday, they were shepherded through the streets by seasoned organizers, often middle-aged men with beards or bruises on their foreheads from prayers. They arranged for rows of marchers holding hands to keep their cohorts packed together within single lanes of traffic. Others linked arms in rows as they marched.
The crowd initially included a mix of women, most of them veiled, and children. But as the marchers rolled through the streets, they shouted to the apartments above, "Come down, come down!" and "One, two, Egyptians where are you?" More men filed out of the buildings as the women and children fell away.
The crowd merged with others as it approached the square and the guides hemmed it until it was a thick mass of thousands stretching for blocks. In the square, a troop of veiled women circled, chanting for the resignation of Mr. Mubarak.
When asked about the Brotherhood's role, the guides demurred, saying the protests represented all Egyptians. But there were mixed feelings in the crowds about the Brotherhood's obvious role that could prefigure future divisions among the momentarily united opposition.
Several protesters said they were glad the Brotherhood could keep up the momentum and discipline when others might fall away or clash with the police.
"The people are too eager; the people are undisciplined," one marcher said. "But the Brotherhood are very organized, very connected, and they have resources."
But others wanted to step away. "I hate the Brotherhood," said Mohamed Ismail, 23, an engineer. "I hate Islamism. I don't want an Iranian regime. I want freedom and democracy."
The government's black-clad security police, a special paramilitary force dedicated to preserving order, began to redeploy around Cairo on Monday, and some protesters said they feared new violence.
"I brought my American passport today in case I die today," said Marwan Mossaad, 33, a graduate architecture student with dual Egyptian-American citizenship. "I want the American people to know that they are supporting one of the most oppressive regimes in the world and Americans are also dying for it."
But after the surprise announcements from the military and Mr. Suleiman, the protest on Tuesday, optimistically dubbed the March of Millions and set to take place around the country, began shaping up as a potentially decisive moment. Mr. Shokry, the former ambassador close to Mr. Suleiman, cautioned that anything could happen.
"What will happen if there is a flare-up, a few bullets shot into the young men, a Molotov cocktail?" he asked. "A million people in the streets. How will we keep the peace?"
(Reporting was contributed by Mona El-Naggar, Kareem Fahim, Anthony Shadid, and Robert F. Worth from Cairo, and Nicholas Kulish from Alexandria.)