Tens of thousands of protesters have packed into central Cairo's Tahrir Square to demand that Egypt's military rulers step aside. The demonstrators want the postponement of elections due to start on Monday. Prime Minister-designate Kamal Ganzouri has said he will not form a new cabinet until after the polls. The latest wave of protests has led to the worst violence since the fall of President Hosni Mubarak in February. More than 40 people have been killed. The Supreme Council of the Armed Forces (Scaf) is overseeing a transition to civilian rule. Despite promises by the council to speed up the process, some protesters fear it intends to cling to power. They want military rule to end before parliamentary elections are held. Yet many Egyptians want the polls to go ahead as planned. One influential group, the Muslim Brotherhood - which is expected to do well in the vote - is not supporting the Tahrir Square protests. Several thousands of people have staged a rival demonstration in favour of the military and elections in Abbasiya Square near the defence ministry, north of Tahrir Square. "Down with Tahrir" and "Yes to the military council", they chanted. In Washington, the White House said power in Egypt should be transferred to civilians "as soon as possible". "The United States strongly believes that the new Egyptian government must be empowered with real authority immediately," a White House statement said. Sunni Islam's highest authority, the grand imam of Cairo's al-Azhar mosque, sent the protesters a rare message of support. An aide, Hassan Shafie, was shown on local TV telling the crowd on Tahrir Square: "The grand imam backs you and is praying for your victory." 'Leave' The Tahrir Square rally follows Friday prayers as well as a week of protests. Tens of thousands took part in what organisers had called a "last chance Friday" rally to demand an immediate transfer of power by the military. "Leave, leave," they chanted, reports the AP news agency. The imam leading the main Friday prayers in Cairo called on the military to hand over power, and said demonstrators would remain in the square until their demands were met, AFP news agency reported. In his first public statement since being named, Mr Ganzouri said he was sure that Scaf leader Field Marshal Mohamed Hussein Tantawi had no desire to stay in power, saying that otherwise, he would not have agreed to become prime minister. Mr Ganzouri, who headed Egypt's government from 1996 to 1999 under Mr Mubarak, said he had been granted greater powers than his predecessors but had not yet begun assembling his ministerial team, although it would be formed within the coming days. Until then, he said former Prime Minister Essam Sharaf, who resigned following the violence earlier this week, would remain in office. Mr Ganzouri's appointment has been heavily criticised by many protesters. "For the second time, we are going to depend upon the old guard of Mubarak's regime. Why do we not give chance for the young, instead of those people who are 80 years old?" one man in Cairo's Tahrir Square, Suhir Nadim, told Reuters news agency. "Appointing Ganzouri is a crisis for the revolution. We must remain in Tahrir," another protester, 44-year-old Hossam Amer, told Reuters. On Tuesday, the head of Scaf, Field Marshal Tantawi, accepted the resignation of the previous military-backed civilian cabinet and announced that presidential elections would be held by June 2012 - six months earlier than planned. The military council has apologised for the deaths of protesters, but insisted that parliamentary polls would start on Monday as scheduled. The Egyptian Independent Trade Union Federation called for a march to Tahrir Square, while another labour rights group called for a general strike to back the protests. Much of the recent violence has taken place in a street leading from Tahrir Square to the interior ministry. Soldiers have now set up barricades of cement, metal bars and barbed wire to separate protesters and security forces. Mr Ganzouri, who distanced himself from Mr Mubarak's regime, has been suggested as a possible presidential candidate. During his term as prime minister, he was known as the "minister of the poor" because he was seen as representing the less well-off, and he remains popular with many Egyptians, says the BBC's Yolande Knell, in Cairo. Monday is to mark the step of an election timetable which lasts until March 2012 for two houses of parliament. The elections will take place in stages around the country - each stage has reportedly been extended to two days.