The head of Egypt's ruling military council, Field Marshal Mohammed Hussein Tantawi, said he had accepted the resignation of the Cabinet and that presidential elections would be held by the end of June.
Mr Tantawi spoke in a televised address on state television.
"The armed forces, represented by their Supreme Council, do not aspire to govern and put the supreme interest of the country above all considerations," he said.
Looking far from confident, he said the army was "completely ready to hand over responsibility immediately, and to return to its original mission to protect the nation if the nation wants that, via a popular referendum, if need be."
Demonstrators in Cairo's Tahrir Square derided the offer, chanting "Leave, leave" after watching the address. More clashes broke out in a nearby street leading to the Interior Ministry.
The response from some protesters was crisp and dismissive.
"Not enough of course," Shadi el-Ghazali Harb, a leader of the Revolutionary Youth Coalition, told Reuters.
"The military council is fully responsible for the political failure Egypt is going through now. We demand a solution that strips the military council of all its powers immediately."
Anger against the generals exploded this month after a cabinet proposal to set out constitutional principles that would permanently shield the army from civilian oversight.
The demonstrators, who again braved clouds of tear gas to occupy Tahrir Square, said the army must relinquish power now.
"We demand a full purge of the system and the removal of the military council," said Fahmy Ali, one protester in Tahrir.
Protesters earlier hanged from a lamp post an effigy of Mr Tantawi, who was Mubarak's defence minister for two decades.
In Egypt's second city of Alexandria, hundreds of protesters marched to a military base waving their shoes in disgust at Tantawi's speech, chanting: "Where is the transfer of power?"
"Tantawi's speech is just like Mubarak's. It's just to fool us," said 27-year-old Youssef Shaaban.
Clashes between police and demonstrators angry at the speech erupted in the eastern city of Ismailia, a witness said.
In a stinging verdict on nine months of army control, London-based rights group Amnesty International accused the ruling Supreme Council of the Armed Forces (SCAF) of brutality sometimes exceeding that of the former regime.
The politicians who attended the discussions in Cairo also said that a parliamentary election, scheduled to start next Monday, would go ahead on time after violence during protests against the ruling military council cast doubt on its timing.
"Presidential elections to be held by the end of June and the final preparations for handing over power by July 1sty," said Emad Abdel Ghafour, head of ultra-conservative Nour (Light) party, adding that he expected the vote on June 20th.
"We agreed July as the month to transfer power to a civilian president," Mr Abdel Ghafour said. "We agreed to accept the resignation of Essam Sharaf's government and to establish a national salvation government."
Mr Sharaf offered his government's resignation yesterday, but there has been no official announcement about whether it had been accepted - nor precisely how a new government of "national salvation" would be made up.
Mr Abdel Ghafour also said controversial proposals put forward by the outgoing army-backed cabinet that would have would have permanently shielded the military from civilian oversight under a new constitution had been dropped.
The White House today called for an end to the "deplorable" violence in Egypt and said elections there must go forward. "We are deeply concerned about the violence. The violence is deplorable. We call on all sides to exercise restraint," White House spokesman Jay Carney told reporters.
The United States gives Egypt's military $1.3 billion a year in aid.
The powerful Muslim Brotherhood, which anticipates a strong showing in the election, attended today's meeting with the military council.
The army's timetable calls for completion of parliamentary elections in March, followed by a six-month period to draw up a constitution before presidential elections are held.
However nationwide demonstrations against army rule have yet to match the vast numbers that turned out to topple Mubarak.
Many Egyptians respect the army and praise its role in easing Mubarak out on February 11th. But tolerance for army rule has worn thin, especially after attempts to set up constitutional principles that would keep the military beyond civilian control.
Political uncertainty has gripped Egypt since Mubarak's fall, while sectarian clashes, labour unrest, gas pipeline sabotage and a gaping absence of tourists have paralysed the economy and prompted a widespread yearning for stability.
Several banks in central Cairo were closed today as a precaution against looting, the state news agency said.
Amnesty International said the military had made only empty promises to improve human rights. Military courts had tried thousands of civilians and emergency law had been extended. Torture had continued in army custody, and there were consistent reports of security forces employing armed "thugs" to attack protesters, it added in a report.
"The SCAF has continued the tradition of repressive rule which the January 25th demonstrators fought so hard to get rid of," said Philip Luther, Amnesty's Middle East and North Africa acting director.
Reuters