Mubarak, who was briefing reporters on Thursday after inaugurating a new port east of Port Said, said he preferred not to discuss individual candidates in the campaign to succeed the late Yasir Arafat.
"But at the end, Fatah has nominated Abu Mazin and I think that he will win," the president said, referring to Abbas by his nom-de-guerre.
Fatah, the largest group in the PLO, endorsed Abbas as its sole candidate to compete in the presidential election, but the group's jailed West Bank leader, Marwan al-Barghuthi, has also announced his candidacy.
Al-Barghuthi, who will run as an independent, had announced only five days earlier that he would not enter the contest.
'Path of peace'
Mubarak also appealed for unity among Palestinians and urged them to set their differences aside in their own interest.
He said he believed Israeli Prime Minister Ariel Sharon was prepared to help the Palestinians organise a credible election, but stressed that the Palestinians should also be helpful.
"But at the end, Fatah has nominated Abu Mazen and I think that he will win"
"The truth is that the Israeli premier said that he was ready to do what was needed to facilitate the election process," Mubarak said. Sharon had expressed readiness to "lift blockades, but he asks for only one thing: that explosions and similar activities end."
Mubarak said: "And I think that if the Palestinians fail to achieve progress during the mandate of the current (Israeli) prime minister, it will be difficult to make any progress, because he is able to follow the path of peace and reach a solution if he wants to."