Speaking in front of thousands, Abbas said "you ask me who killed him, I know – but my testimony alone is not enough."
"A commission of inquiry is digging into that, but you'll find out at the earliest opportunity and be amazed when you know who did it."
Palestinians to open museum to longtime leader Arafat
"I do not want to mention names, because these names do not deserve to be remembered," he added.
Arafat rose to become the leader of the Palestinian movement in the late 1960s, leading an armed struggle against Israel.
He died on November 11, 2004 at a hospital near Paris from unknown causes at the age of 75.
More than a decade after his death, he remains a towering figure in Palestinian culture, politics and society.
Next war in Gaza will be the last: Israeli defence minister
The Palestinians have long accused Israel of poisoning him, charges the Israeli government firmly denies.
His body was exhumed in 2012 for tests but a subsequent French investigation found no proof of poisoning.
The Palestinians rejected that report, citing apparent inconsistencies between the French findings and separate ones from Switzerland and Russia that gave currency to alleged poisoning by polonium.
Abbas and his longtime rival Mohammed Dahlan have both accused each other of complicity in Arafat's death in the past.
Abbas's comments came with some Arab countries reportedly pressuring the 81-year-old to allow Dahlan, who has been in exile in the United Arab Emirates, to return to the West Bank.
Those moves come amid talk of who will succeed Abbas.
Sources in Abbas' Fatah movement said Arafat's death could be discussed at the party's seventh annual conference, with the commission of inquiry potentially announcing its conclusions.
The conference will be held on November 29.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ