The Brotherhood candidate, Mohammed Mursi, has a slight lead on former PM Ahmed Shafiq, with a reported 25.3% of votes against 24.9%.
The two represent forces that have battled each other for decades.
Mr Shafiq pledged there would be “no going back” to pre-revolutionary Egypt.
“I pledge now, to all Egyptians, we shall start a new era. There is no going back,” he was quoted by AFP news agency as saying. “We must accept the results.”
Voting in the first round took place peacefully on Wednesday and Thursday.
The official results will be announced on Tuesday, but state media have been reporting tallies from polling stations around the country and have now confirmed the two frontrunners.
The vote was hailed as a historic achievement by international observers but the BBC’s Jon Leyne in Cairo says many Egyptians – particularly supporters of the revolution – will find the choice they have been left with most unappealing.
Former US President Jimmy Carter, who led a delegation of election observers, said in spite of some violations the polls had been “encouraging”.
A spokesman for the Muslim Brotherhood said Egypt would be “in danger” if Mr Shafiq won, and the group would reach out to other candidates to defeat him.
Warning of “determined efforts to recreate the old regime”, the Brotherhood urged parties that supported the uprising that overthrew Hosni Mubarak to unite around their candidate.
They have invited a range of opposition figures to a meeting on Saturday.
Both the Brotherhood and Shafiq campaigns have accused each other of “stealing” the revolution.
Shafiq spokesman Ahmed Sarhan urged pro-revolutionaries to vote for his candidate, saying that while his programme was about “the future”, the Brotherhood’s was about “an Islamic empire”.
The polarised choice remaining in the run-off suggests Egypt could be entering a new period of confrontation, our correspondent says.
Ahmed Khairy, spokesman for the Free Egyptians Party, a secular liberal party which emerged last year, said the outcome of the first round was “the worst possible scenario”, reported Egyptian newspaper al-Ahram.
He described Mr Mursi as an “Islamic fascist” and Mr Shafiq as a “military fascist”.
The pro-revolution vote was split, the reported results suggest, between leftist Hamdin Sabbahi (third with 21.5%) and a moderate Islamist who broke with the Brotherhood, Abdul Moneim Aboul Fotouh (fourth with about 19%).
Fears of friction
Mr Sabbahi dominated in many urban areas, including Alexandria, local reports suggested.
Former Arab league chief Amr Moussa trailed in fifth place.
Mr Mursi and Mr Shafiq represent very different strands of Egyptian society.
Mr Mursi is seen as belonging to a popular strand of political Islam that was excluded from the political process for many years under Hosni Mubarak.
Mr Shafiq, who served briefly as Mr Mubarak’s prime minister, is regarded by many as a creature of the old secular regime.
Analysts say he drew his support from people fearful of an Islamist takeover, and those exhausted by the upheavals of the past 16 months.
About 50 million people were eligible to vote in the polls, in which 13 candidates were vying for the presidency.
It was the country’s first freely contested presidential election in its history, and observers said it had been conducted peacefully.
The military body that assumed presidential power in February 2011 – the Supreme Council of the Armed Forces (Scaf) – has promised a fair vote and civilian rule.
Until a new constitution is approved it is unclear what powers the president will have, prompting fears of friction with a military which seems determined to retain its powerful position.
Many Egyptians have grown frustrated with the pace of change in their country following the revolution, as the economy languishes, public services break down and crime levels rise.