The vote for both the party's central committee and its parliament, known as the revolutionary council, came after Abbas opponents were excluded from the election.
Beginning on Tuesday, some 1,400 delegates met in Ramallah for Fatah's first congress since 2009 and to vote in the elections.
At the congress's opening, Abbas was re-elected head of the party.
Following Yasser Arafat's death in 2004, the ageing leader has been in charge of Fatah, the Palestine Liberation Organisation and the Palestinian Authority.
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Dahlan is currently in exile in the United Arab Emirates and Abbas reportedly resisted pressure from Arab nations to allow him to return.
Observers saw the reduced number of delegates eligible to vote -- down from more than 2,000 in 2009 -- as part of a move to exclude Dahlan supporters.
The central committee includes 18 members, plus four who are appointed, and the parliament will have 80 elected members and around 40 who are appointed.
Other key figures standing included Jibril Rajoub, a former head of intelligence who now leads the Palestinian Football Association. He secured the second-highest number of central committee votes at more than 800.
Saeb Erekat, secretary general of the Palestine Liberation Organisation and a close Abbas ally, was also re-elected to the committee.
Arafat's nephew Nasser al-Kidwa, also mentioned as a possible successor to Abbas, was re-elected to the central committee as well.
He was elected to a four-year term as Palestinian president in 2005, but has remained in office as elections have not been held.
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