Final election results are expected in the next few days, though ruling military authorities in Cairo delayed the official tally at least once.
The Muslim Brotherhood claims its Freedom and Justice Party won at least 40 percent of the vote while the conservative al-Nour Party staked its claim to 30 percent of the vote for the lower house of Parliament.
Runoff contests are expected and the Muslim Brotherhood said in earlier statements that some polling stations were ill-equipped and there were irregularities.
The Muslim Brotherhood took 20 percent of the seats in the Egyptian Parliament by running as independent candidates in 2005. It lost its political leverage during the last election under the regime of Hosni Mubarak during a 2010 vote, however.
Jon Alterman, director of the Middle East program at the Center for Strategic and International Studies, told Bloomberg News that Islamist parties were good at mass appeal but not be so politic savvy.
"The problem that all these parties will have is, how do you convert those sentiments into laws and policy? I don't think they figured that out," he was quoted as saying.
The elections were preceded by protests over the perceived reluctance of the military-led government to cede authority to civilians. Samer Soliman, a member of the political Egyptian bloc, told the news agency the rise of Islamic parties in the country was scaring many Egyptians. There were concerns, he added, that they bought the election through "electoral bribes."