Cairo (CNN) -- Results of the first round of voting from Egypt's historic election are being postponed, the country's military rulers said Thursday. The announcement will come Friday or Saturday, said Amir Imam, spokesman for the Supreme Council of the Armed Forces. The first voting since the fall of President Hosni Mubarak took place Monday and Tuesday, the first in a multi-step process to pick members of the lower house of Parliament. Those lawmakers will be tasked with drafting a new constitution. Two Islamist parties, the Muslim Brotherhood and Al Noor Salafi, have claimed a lead in ballot counting, but officials are tight-lipped about any results. This week marked the first time some Egyptians -- young and old -- had ever cast ballots after three decades of rule under Mubarak, who was ousted in February after weeks of protests. Some voters and human rights activists expressed hope that their votes will actually count, though some boycotted the elections saying they don't trust the voting will be free and fair. There were reports of some illegal campaigning taking place, with the Egyptian Association of Human Rights alleging some cases of vote-buying in the city of Alexandria. Elections for Egypt's lower house of Parliament are scheduled to take place in three stages, based on geography. The last of the three stages is set to take place in January. Upper house elections will run between January and March. Presidential elections will be held by June, according to the Supreme Council of the Armed Forces, Egypt's acting ruling body. Military leaders have said they will hand over power to a new government when one is elected, but many Egyptians say they don't trust the council and fear the military will cling to power. During the past two weeks, at least 42 people have been killed in clashes, as protesters called for an immediate end to military rule. An additional 3,250 have been wounded, according to the Health Ministry.