"For those who are discussing whether I'm alive or not, how I'm doing - right now it's the weekend, second half of August 2023, I'm in Africa," Prigozhin says in the short video.
In a call with reporters, Kremlin spokesman Dmitry said that Russia's investigation took into account the possibility that the crash had been caused deliberately.
The pilot, named Maj. Andrii Pilshchykov and known by the call sign of Juice, was part of the Ghost of Kyiv unit and dreamed of Ukrainian pilots flying F-16s.
Days after he had been presumed dead, Russia finally confirmed the Wagner leader's demise.
The crash occurred on Friday over the Zhytomyr region, which lies west of Ukraine's capital Kyiv.
The fate of the complex, lucrative web of military and commercial operations that Prigozhin and Wagner created hangs in the balance.
The Federal Security Service is Russia's primary security agency. It is Russia's successor to the KGB of the Soviet Union.
Russian investigators opened a criminal probe. Some unnamed sources told Russian media they believed the plane had been shot down.
All ten people on board the aircraft died in the crash, according to the Russian Emergency Situations Ministry.
The first helicopter landed safely after the collision but the second one crashed, killing all three people who were on board.