The army sought to stave off pressure from jubilant protesters to swiftly hand power to a civilian-led administration by saying that it is committed to a "free democratic state".
The military leadership gave no timetable for the political transition, and many of the demonstrators who filled Cairo's Tahrir square for 18 days rejected the military's appeal to dismantle the barricades and go home.
They said they were waiting for specific commitments from the military on their demand for a civilian-controlled interim administration, the lifting of the oppressive state of emergency and other steps toward political liberalisation.
The shock waves of Mubarak's fall were felt across the region today, particularly in Algeria and Yemen. Thousands of anti-government protesters, apparently inspired by events in Cairo, turned out in Algiers to confront the police. There were reports that hundreds had been arrested. In Sanaa, a protest by about 2,000 people to demand political reform was broken up by armed government supporters.
Some of the organisers of Egypt's revolution announced they had formed a council to negotiate with the military and to oversee future demonstrations to keep up the pressure on the army to meet the demand for rapid democratic change.
"The council will have the authority to call for protests or call them off depending on how the situation develops," said Khaled Abdel Qader Ouda, one of the organisers.
Earlier, General Mohsen el-Fangari said in a televised statement that the military intends to oversee "a peaceful transition of power" to allow "an elected civilian government to rule and build a free democratic state". He said the present cabinet would continue to sit until a new one is formed.
El-Fangari announced that the widely-ignored overnight curfew imposed during the crisis would be shortened by several hours.
The military council also sought to allay American and Israeli concerns by saying that Egypt will continue to respect international treaties it has signed. Israeli politicians had expressed concern that a new government in Cairo might abrogate the 1979 peace accord between the two countries.
Israel's finance minister, Yuval Steinitz, welcomed the announcement.
"Peace is not only in the interest of Israel but also of Egypt. I am very happy with this announcement," he told Israeli television.
But there will still be concern in Jerusalem about whether a future civilian government will be as cooperative as Mubarak's regime in isolating and undermining the Hamas administration in the Gaza strip.
People continued to pour in to Cairo's Tahrir square, in part to celebrate at the epicentre of the revolution against the Mubarak regime. But there was also concern among some of the core group of activists who helped organise the mass protests that brought down Mubarak at the army's apparent intent to control the political transition.
A group of the activists issued what they called the "People's Communique No 1" — mirroring the titles of military communiques – listing a series of demands.
The included the immediate dissolution of Mubarak's cabinet and "suspension of the parliament elected in a rigged poll late last year".
The reformists want a transitional administration appointed with four civilians and one military official to prepare for elections in nine months and to oversee the drafting of a new constitution.
The Muslim Brotherhood, the banned Islamist group that has been the target of military tribunals aimed at suppressing it, sought to allay fears in Egypt and abroad that it will attempt to take power.
It said it would not be running a candidate in presidential elections and would not seek to win a majority in parliament. It also offered unusual support for the military council.
Reuters reported that the information minister, Anas El-Fekky, was placed under house arrest the day after the military barred some Egyptian officials, including former ministers and state bankers suspected of corruption, from leaving the country without the permission of the armed forces or the state prosecutor.
Mubarak was believed to be at his luxury retreat in Sharm el-Sheikh.
One of the most urgent tasks for the new Egyptian administration is to get the economy back on track. The protests of the past three weeks are estimated to have cost the country more than $300m a day, in part because of a collapse in tourism.
The authorities announced that the stock exchange will reopen on Wednesday.