A spokesman for the US-led anti-IS coalition said he could not confirm the Russian claim.
He emerged as the leader of al-Qaeda in Iraq, one of the groups that later became Islamic State of Iraq and the Levant (IS), in 2010.
He said Abu Yasin al-Masri is the same person as Abu al-Haj al-Masri, who the Russians on Friday said they killed near Raqqa in May.
The strike is believed to have killed several other senior leaders of the group, as well as around 30 field commanders and up to 300 of their personal guards, the Russian defense ministry statement said.
The Russian statement said that the strike targeted ISIS leaders as they met to discuss their exit from the city through the so-called southern corridor.
The United States said it could not immediately confirm whether Baghdadi, the undisputed leader of global jihadism, was dead.
"His death has been reported so often that you have to be cautious till a formal Daesh statement comes", a European security official said, using an Arabic acronym for the group. There was no mention al-Baghdadi.
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Iraqi intelligence officials said the authorities were checking the report and would announce his death if it received "solid confirmation".
Al-Hashimi said the other Isis leader, al-Beljiki, was unlikely to have been in Syria at the time of the attack.
A USA -led coalition is assisting Iraqi forces in the Mosul battle and supporting the Syrian Democratic Forces (SDF), which includes Arab and Kurdish militias, in Raqqa.
If confirmed, his death would mark a major military success for Russian Federation, which has conducted a military campaign in support of Syrian President Bashar Assad since September 2015.
Su-35 and Su-34 jets were used in the strike, which was preceded by drone reconnaissance flights, the ministry said.
Abu Bakr al-Baghdadi, which is a nom de guerre, was born Ibrahim Awwad Ibrahim Ali al-Badri al Samarrai.
It added that Washington was informed in advance about the place and time of the strike near the jihadists' Syria stronghold, which is now under assault by US-backed fighters.
Information for this article was contributed by Bassem Mroue, Lolita C. Baldor and Robert Burns of The Associated Press.
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