Fatah, the oldest Palestinian party, is holding its first congress in seven years at a time when Abbas is seeking to quell dissent in the face of internal rivalries.
The 81-year-old has not publicly designated a successor, and the vote will be an indicator of the strengths and weaknesses of the various factions in Fatah.
Casting his ballot on Saturday afternoon, Abbas called the process "democratic and transparent".
According to a recent poll, two-thirds of Palestinians are dissatisfied with Abbas and want him to resign.
The congress comes with the Israeli-Palestinian peace process at a standstill since a US-led initiative collapsed in April 2014.
The 1,400 delegates voted at Abbas's Ramallah headquarters in the Israeli-occupied West Bank and also in the Gaza Strip where several dozen were stranded after Israel refused them passage through its territory to Ramallah.
They are to choose 18 members of the party's Central Committee, its highest body. Abbas will appoint another four.
The congress will also elect 80 members of the Fatah Revolutionary Council -- the party's parliament. Another 40 council members are directly appointed.
Congress spokesman Mahmoud Abu al-Hija said later Saturday that voting had ended and the count was under way.
"The count started in the evening," he said. "The results should be announced at the concluding session on Sunday."
Founded in 1959, Fatah is the backbone of the Palestine Liberation Organisation (PLO) which the international community considers the representative of all Palestinians.
Analysts say the party's rival factions include supporters of Abbas's longtime rival Mohammed Dahlan, currently in exile in the United Arab Emirates.
Abbas was elected president in 2005 for what should have been a four-year term.
But there have been no elections since then, and with his hold on power drawing increasing internal dissent, observers say he is seeking to ready a successor.
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- 'A different voice' -
Social networks and some local news media during the week published names of candidates in the vote who they say have prior approval from Abbas and were therefore guaranteed election even before polling began.
Abu al-Hija denied the allegations.
At the opening session on Tuesday, members re-elected Abbas party head by consensus.
Observers see 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.
Dimitri Diliani, elected to the Fatah Revolutionary Council in 2009, has said he was not invited to the congress like dozens of others because "we bring a different voice".
He said a planned press conference at a refugee camp near Ramallah on Tuesday with those recently dismissed from the party had been called off after threats "from the security services", including death threats.
The previous congress in 2009 brought into the ruling bodies veterans of the Palestinian security services such as Dahlan, Jibril Rajoub and the hugely popular Marwan Barghouthi, who is serving five life sentences in an Israeli prison.
This year Barghouthi is standing again, as is Rajoub who, as head of the Palestinian Football Association, is active on the international stage.
So too is Saeb Erekat, Abbas's number two in the PLO hierarchy.
Dahlan and his backers have been thrown out of Fatah.
Abbas told the congress on Wednesday he remained committed to dialogue with Israel but that it would not come at the expense of Palestinian principles.
"We are saying to the Israeli people that we want peace that conforms to international resolutions, but it is your government who does not," he said.
Israel must "recognise that settlements are illegal", he said, adding that "our hand will remain extended for peace".
That policy enjoys consensus support in Fatah, which renounced violence several years ago. The rival Hamas Islamist movement which controls the Gaza Strip pursues a policy of armed conflict with Israel.