Brotherhood officials said the results it had obtained late Sunday from more than 1,200 of the country's approximately 13,000 polling stations, which were unofficial and unconfirmed independently, gave Mohamed Morsi 842,577 votes to former Prime Minister Ahmed Shafiq's 541,785, the Los Angeles Times reported.
The Arab satellite television channel al-Jazeera reported Morsi was ahead with 60 percent of the vote, but those totals did not include Egypt's largest cities, the Times said.
A Shafiq campaign official said in a Twitter posting, "Shafiq is on the cusp of becoming Egypt's first post-Jan. 25 president … Indications are very promising."
It won't be until Wednesday or Thursday before official results are posted.
The two-day presidential runoff was marred by allegations of illegal campaigning by both candidates.
Shafiq has campaigned on a platform of returning Egypt to stability and law and order. Morsi has promised economic and political reform.
The country was plunged into further political chaos Saturday when the Supreme Council of Armed Forces declared the Parliament null and void in accordance with a court ruling issued Thursday, Israel Radio said. The Muslim Brotherhood called the dissolution of Parliament a dangerous step and demanded a referendum on the issue, the BBC reported.
Soon after the polls opened Saturday, the presidential campaigns accused each other of vote-buying, illegal campaigning and rigging votes, Ahram Online reported. Presidential Electoral Commissioner Farouq Sultan confirmed both candidates had committed violations, the Egyptian Web site said.
Some 53 organizations are observing the election, including groups from the United States and South Africa, CNN said.