Igor Konashenkov, a spokesman for the Russian Defense Ministry, said the US had offered no verifiable proof of Baghdadi's death in the raid that US President Donald Trump announced on Sunday.
Over the years, Baghdadi had been reported dead on a number of occasions. In 2016, the US Department of State offered a reward of up to $25 million for information leading to his capture or death. Even if Baghdadi were killed, the Russian Defense Ministry questioned the extent to which his death would affect events in Syria.
Trump said Baghdadi, who had led the Islamic State since 2010, killed himself by detonating a suicide vest during the raid in Syria by US Special Operation Forces.
Konashenkov said that contradictory information was emerging over the details of the raid, reinforcing doubts that the operation took place.
In his announcement, Trump expressed his gratitude to Russia, Turkey, Syria, Iraq and the Syrian Kurds, saying the mission could only have taken place with their help.
But Konashenkov said he knew nothing about the supposed US cooperation with Russia.
"We know nothing about any assistance regarding the flight of US aircraft in the airspace of the Idlib de-escalation zone in the course of this operation," he said, adding that no airstrikes by the US Air Force or by the US-led coalition had been reported from that zone on Saturday or on other recent days.
That aside, the Russian Defense Ministry said it doubted that Baghdadi could have hid in territory controlled by the Jabhat al-Nusra group in Idlib.
"This organization has always unhesitatingly killed IS fighters on the spot as key rivals for power in Syria," Konashenkov said. "Keeping this in mind, the US or other participants in the operation should at least provide direct evidence that the former Islamic State leader had been safely staying in territory controlled by the 'Syrian al-Qaida'."
The Kremlin has refused to confirm or in any way comment on the reports about Baghdadi's death. In response to media questions, Dmitry Peskov, the press secretary of President Vladimir Putin, said: "See what Konashenkov said."
Meanwhile, US magazine Newsweek reported on Monday that Abdullah Qardash may be a possible successor to Baghdadi.
Russian authorities and experts agree that even if the US claim of Baghdadi's death is true, his passing will have little impact in Syria.
"After the IS was ultimately defeated by the Syrian government army with the support of the Russian air force in early 2018, yet another 'death' of Baghdadi will have no impact either on the situation in Syria or on the actions of the terrorists staying in Idlib," Konashenkov said.
Vladimir Fitin, head of the Near and Middle East Center at the Russian Institute for Strategic Studies, said the claimed death of Baghdadi won't put an end to the activities of IS. "The Americans have buried Baghdadi more than once. It is yet to be proved what really happened," he said.
"Anyway, as experience shows, the extermination of a leader does not mean the extermination of the corresponding organization. This has been seen in the example of al-Qaida and other terrorist groups."