Mubarak's recently appointed cabinet will remain until a new administration is set up.
Military pledges civilian rule for Egypt
A senior army officer, speaking on behalf of The Supreme Council of the Armed Forces, also said on state television that the cabinet appointed by Mr Mubarak in his final weeks would stay until a new one could be formed.
Whether the country's relatively anonymous top military officers will willingly give up their new-found control and usher in the democratic reforms expected by about 84 million Egyptians has been - and remains - an open question.
The Supreme Council, which is made up of the top generals of each branch of the military and headed by the defence minister, Field Marshal Mohammed Hussein Tantawi, said it did not intend to take the place of the civilian Egyptian government.
It would instead, said Gen Mohsen el Fangari, "look to guarantee the peaceful transition of power in the framework of a free, democratic system which allows an elected, civilian power to govern the country to build a democratic, free state".
The council also emphasised it stood by previous commitments, which included a pledge to end a 29-year state of emergency and "all regional and international obligations and treaties".
Egypt's treaties include a 1979 peace accord with US ally Israel, which has been watching developments in Egypt with concern.
The United States, Egypt's top ally, is also eager to ensure the accord remains in place. The military strongly supports the accord, not in small part because it guarantees US aid for the armed forces, currently running at US$1.3 billion (Dh4.77bn) a year.
Anti-Israeli feeling is strong in Egypt, and many of the hundreds of thousands of protesters expressed anger at Mr Mubarak's close co-operation with Israel on a range of issues. Still, few seriously call for the abrogation of the peace treaty, realising the international impact.
Gen el Fangari also said the current government had been asked by the military to continue operating until a new one was formed, which appeared to be a stop-gap measure to keep the state and struggling economy functioning while a transitional administration is set up.
"The current government and governors undertake to manage affairs until the formation of a new government," he said, in front of a row of Egyptian military and national flags, although he did not say when a new government would be formed.
The military's statement had been eagerly awaited by the public and thousands of protesters still massed in Cairo's central Tahrir Square.
The crowds were still riding high on jubilation after prompting Mr Mubarak's resignation on Friday after 18 days of unprecedented protests.
Some picked up brooms and swept the streets; others took down tents, smiling and chatting about their new political era. Among them were those determined to stay, waiting for a clear signal from the army that it would follow through on the promised reforms.
"The people want a civilian government, not someone like Mubarak, a soldier who ruled in normal clothes," said Amir Raouf, 48, an architect from Cairo. "This revolution is being led by the internet generation, and this new generation will never accept permanent rule by the military."
"We've reached a very difficult point now," said Hani El Mamsi, a 33-year-old accountant. "We need the military to maintain the stability here until we have elections. I hope they stay as long as they can, because you know they don't want to be guarding museums and streets. The military is supposed to protect against outside threats."
The Muslim Brotherhood, Egypt's banned Islamist group, praised the military's intentions in a statement after voicing worries a day earlier.
The people, the Islamist organisation said, trust "that the army will continue during this transitional period, to work in favour of each and every Egyptian in a peaceful manner to establish a civil state and legislative institutions chosen by the people through free, fair and transparent elections".
In Washington, the US president, Barack Obama, praised the military's performance so far but called for "a transition that is credible in the eyes of the Egyptian people.
"That means protecting the rights of Egypt's citizens, lifting the emergency law, revising the constitution and other laws to make this change irreversible, and laying out a clear path to elections that are fair and free," said Mr Obama, who has dispatched a senior military adviser, Admiral Mike Mullen, the chairman of the Joint Chiefs of Staff, to the Middle East to reassure two key allies - Jordan, facing its own rumblings of civil unrest, and Israel, which sees its security at stake in a wider transformation of the Arab world.
The history of the Middle East is littered with examples in which the military took control of the government and never followed through on promised reforms and elections, sceptics point out. And Egypt's military has a lot invested in the status quo.
Over the past several decades, Egypt's military has expanded into the civilian economy and now produces billions of dollars worth of consumer goods in vast factories, owns resorts and hotels on the Red Sea, and has installed many of its top former officers in executive positions in large companies across the country.
A key test of the military's intentions, analysts say, will be its approach to lifting the state of emergency that has been in place since the October 1981 assassination of president Anwar Sadat and grants the government the authority to detain dissidents and suspected militants without trial, suspend the right to free assembly, shut down newspapers and other media, and seize private commercial interests.
Facing a mobilised citizenry and strong international pressure, and lacking a recent tradition of direct involvement in Egyptian politics, the military had little incentive to deviate from its promises, said Amr Hamzawy, a veteran Egyptian political expert at the Carnegie Middle East Center in Beirut who helped mediate talks between the opposition and Mr Mubarak's regime.
"The fact that the people are really mobilised, they cannot be played with power games," he said. "I guess [the army] feels at ease withdrawing from politics again, and there have been a lot of encouraging signs, especially the fact that they have not announced any escalation in martial law."