Anti-government protesters in Egypt have stormed the national headquarters of President Mohammed Morsi's Muslim Brotherhood in the capital, Cairo.People are reported to have ransacked the building in the eastern Moqattam district and also set it on fire.Eight people have been killed outside since Sunday, security sources say.Earlier, the opposition movement behind the protests that saw millions take to the streets across Egypt on Sunday gave Mr Morsi until Tuesday to resign.Tamarod (Rebel) said Mr Morsi would face a campaign of civil disobedience if he did not leave power and allow elections to be held.Protesters across Egypt have accused the president of failing to tackle economic and security problems since being elected a year ago. His supporters have insisted he needs more time.Staff evacuatedMillions of people attended demonstrations across the country on Sunday to demand Mr Morsi step down.The crowds seen in Cairo's Tahrir Square were the biggest since the 2011 revolution that toppled Hosni Mubarak.Sporadic outbreaks of violence were reported nationwide. Four people were killed in the central province of Assiut, while security sources told BBC Arabic that eight people had died in clashes around the Muslim Brotherhood's headquarters in Moqattam since Sunday evening.Overnight, protesters threw petrol bombs and rocks at armed guards inside, who retaliated by firing at them.On Monday morning, the protesters stormed the six-storey building and began throwing objects of broken windows. One protester was seen removing the Muslim Brotherhood sign, while an Egyptian flag was flown from a balcony.Witnesses told the AFP news agency that no members of staff had been inside the building when it was stormed because they had been escorted out earlier.The movement's leaders have complained that the police have failed to protect its headquarters.'Constitutional legitimacy'Earlier, Tamarod issued a statement saying the protesters would give Mr Morsi until 17:00 (15:00 GMT) on Tuesday to leave power and allow state institutions to prepare for early presidential elections.Otherwise, people would begin a campaign of "complete civil disobedience", the group warned.It urged "state institutions including the army, the police and the judiciary, to clearly side with the popular will as represented by the crowds".The group also rejected offers of dialogue from the president."There is no way to accept any half measures," it said. "There is no alternative other than the peaceful end of power of the Muslim Brotherhood and its representative, Mohammed Morsi."On Saturday, Tamarod said it had collected more than 22 million signatures - more than a quarter of Egypt's population - in support.But Mr Morsi was defiant in an interview published on Sunday, rejecting the opposition calls for early presidential elections."If we changed someone in office who [was elected] according to constitutional legitimacy - well, there will be people opposing the new president too, and a week or a month later they will ask him to step down," he told the Guardian newspaper.He said he would not tolerate any deviation from constitutional order."There is no room for any talk against this constitutional legitimacy. There can be demonstrations and people expressing their opinions," he added. "But what's critical in all this is the adoption and application of the constitution. This is the critical point."