"The report rules out the poisoning theory and goes in the sense of a natural death," the source said.
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Israeli Foreign Ministry spokesperson Yigal Palmor said the findings were "not a surprise."
The French experts' findings differ significantly from those of Swiss scientists, who said last month that their research offered some support for the suggestion Arafat was killed by polonium poisoning.
Arafat died at a French military hospital near Paris on November 11, 2004, with doctors unable to say what killed him. At the time, an autopsy was never carried out – at his widow's request.
But France opened a formal murder inquiry into his death in August 2012, a month after an Al-Jazeera documentary linked his death to polonium poisoning.
Some 60 samples were taken from Arafat's remains in November 2012 and divided between Swiss and Russian investigators and a French team carrying out a probe at his widow's request.
The Swiss team said the test results neither confirmed nor denied polonium was the actual source of his death, although they provided "moderate" backing for the idea he was poisoned by the rare and highly radioactive element.
They said the quantity of the deadly substance found on his remains pointed to the involvement of a third party.
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