The returns show Mohammed Morsi with 52 percent of the vote and former Prime Minister Ahmed Shafiq with 48 percent. A million votes separated the two.
A brotherhood spokesman said the remaining votes could not make up the difference. The official results are expected by Thursday.
Meanwhile Egypt's ruling military council pledged Monday to honor its promise to hand over power to the newly elected president by the end of this month.
Maj-Gen. Mohammed al-Assar, a senior member of the ruling council, said the generals would transfer power in a "grand ceremony." He did not give an exact date or mention Morsi by name.
The Associated Press contributed to this report.