Bikyamasr.com reported it appeared the Freedom and Justice Party would garner the most seats with the more conservative Islamist el-Noor Party coming in second and the more liberal Egyptian Bloc coalition third.
The Egyptian news Web site said official results in the first of three phases of voting won't be known until Thursday.
The Egyptian newspaper al-Masry al-Youm reported Freedom and Justice Party leaders were quick to stake a claim on forming the country's new national salvation government.
"It is the majority in Parliament that has the right to form the government," party legal adviser Ahmed Abu Baraka said.
Others sought to parry the Muslim Brotherhood's power move.
"It's premature for the Brotherhood to claim that right," Yousry Hammad, spokesman for the Salafi Nour Party, told al-Masry al-Youm.
With Egypt looking to reform its government since the overthrow of President Hosni Mubarak, tensions have been running high and protests have turned violent.
Mohammed el-Sherbeeny, a Health Ministry spokesman, told Ahram Online Wednesday 108 people were injured, 10 seriously, in clashes that erupted when scores of armed men attacked protesters staging a sit-in in Cairo's Tahrir Square late Tuesday as the second day of voting in parliamentary elections came to an end.
"I can see Molotov [cocktails] thrown into the square and I hear gunshots fired. There are also people standing on top of 6 October bridge, which overlooks the square, and they are throwing stones at protesters," Mohammed el-Badry, a member of the General Secretariat of the Revolution, told Nile TV.
He said two people were shot in the eye and were taken to nearby field hospitals for treatment. No military forces or police intervened, he said.