The Brotherhood's political arm also distanced itself from an ultraconservative Islamist party as vote tallies indicated the two parties would together make up a parliamentary numerical majority.
The official results from the first of three rounds of voting for the Parliament's lower house were to be announced Friday, Egyptian authorities said. The first round included Egypt's two biggest cities, Cairo and Alexandria.
The results release was to coincide with a large Tahrir Square protest demanding the ruling generals relinquish power.
There is no "alleged alliance" with the Salafi al-Nour Party to form "an Islamist government," the Brotherhood's Freedom and Justice Party said in a statement ahead of the results release.
The al-Nour Party maintains an exacting version of Islam, with governance based on its understanding of the Koran, Islam's sacred book, and Sunnah, examples the Prophet Mohammed taught and instituted.
While the Brotherhood emphasizes tolerance and pluralism, the Salafis talk about putting into effect an Islamic religious code on matters such as banking, alcohol, women's dress and entertainment.
The elections "will most likely lead to a balanced Parliament that reflects the various components of the Egyptian public," the Freedom and Justice Party statement said, promising to work across the political spectrum to facilitate a smooth transition to civilian government.
The state news media indicated the Brotherhood's party would likely win about 40 percent of the votes, the Salafi party about 25 percent and a liberal, social democratic coalition known as the Egyptian Bloc slightly less than 25 percent.
The Egyptian Bloc was created to prevent the Brotherhood's party from winning the parliamentary elections.
The Brotherhood party said it would not let Parliament become a rubber stamp for the ruling Supreme Council of the Armed Forces, which has clung to power despite two weeks of anti-junta protests and violent street clashes.
Senior party members told the British newspaper The Guardian the generals risked further unrest if they defied the people and failed to return to their barracks next year.
"Egypt is currently going through a critical era in its history, and I am confident the military will choose to cooperate with Parliament and not confront it -- any other path will create more chaos," Freedom and Justice Party Vice President Essam al-Arian said.
"SCAF currently wields executive and legislative power," Amr Darrag, the party's chief in Giza, Egypt's third-largest city, told The Guardian. "As soon as Parliament convenes, the latter must be passed to the institution democratically elected by the Egyptian people."
2014: The Year in Music [PHOTOS]