The cabinet offered to resign on Monday after three days of protests.
However, the Mena news agency said the resignation had not been accepted by the military council.
An official statement said that ''owing to the difficult circumstances the country is going through, the government will continue working.''
Earlier, Culture Minister Emad Abu Ghazi resigned in protest because of the way the situation is being handled.
Large crowds gathered again in Tahrir Square in Cairo on Monday because they fear the interim military government has hijacked the revolution which toppled President Hosni Mubarak.
Troops and police have used force to try to disperse the demonstrators.
Members of 25 political parties on Monday called for the ministers of information and the interior to be sacked.
At least 33 people have died during the demonstrations in Cairo.
The Supreme Council of the Armed Forces, led by Field Marshal Mohamed Tantawi, is charged with overseeing the country's transition to democracy.
The BBC reports calls for Field Marshal Tantawi's resignation could be heard during the weekend events.
It is the longest continuous protest since President Mubarak stepped down in February.
Clashes also took place in other cities over the weekend, including Alexandria, Suez and Aswan.
Morgue officials said on Monday that the death toll was now at least 33. Some 1750 people were injured.
Parliamentary elections begin on 28 November and will be staggered over the next three months.
A statement from the cabinet on Sunday said the elections would go ahead as planned.
