The reliability of the Brotherhood's polls could not be confirmed. Regional television channels, citing their own exit polls, also placed Morsi as the top finisher, with rivals Ahmed Shafiq and Hamdeen Sabahi vying for second post.
Shafiq, a former air force commander, was Mubarak's last prime minister and was himself forced from his post by protests soon after his former boss. Opponents brand him as a feloul or "remnant" of the old autocratic regime, but he has drawn support from Egyptians who crave stability or fear Islamists.
Sabahi is a leftist who had been a dark horse but gained steadily in opinion polls over the last week, attracting Egyptians who want neither an Islamist nor a former regime figure.
The Brotherhood is hoping that a victory in the presidential race will seal its political rise since its longtime opponent Mubarak was ousted on Feb. 11, 2011, in a wave of protests. The group won just under half the seats in parliament in elections held late last year, establishing it as the biggest political bloc.
But it had troubles in the presidential campaign. Its first choice for candidate, deputy leader Khairat el-Shater, was disqualified because of a Mubarak-era conviction. Morsi was the Brotherhood's second choice and was seen as less charismatic.
He also faced competition for religious voters from Abdel-Moneim Abolfotoh, a moderate Islamist who split from the Brotherhood last year and has also drawn liberals with his more inclusive vision.
One of the prominent secular candidates, former Foreign Minister Amr Moussa, made an emotional appeal three hours before voting ended, urging supporters to get to the polls. The last-minute call suggested his exit polls were not going his way.
Earlier, Moussa gave a surprise interview to Al-Arabiya television, calling on Shafiq - his main rival for the secular vote - to drop out of the race. Rattled, with his hair unkempt, Moussa launched a scathing attack on Shafiq, saying that if elected Shafiq would "re-create" the Mubarak regime.
Both Shafiq and the Brotherhood's Morsi have repeatedly spoken of the dangers, real or imaginary, of the other becoming president. Morsi has said there would be massive street protests if a feloul wins, arguing it could only be the result of rigging.
Shafiq, on his part, has said it would be "unacceptable" if an Islamist takes the presidential office, echoing the rhetoric of Mubarak, his longtime mentor who devoted much of his 29-year rule to fighting Islamists. Still, Shafiq's campaign has said it would accept the election's result.
If a runoff is held, the final result would be announced on June 21.