Prigozhin died when his business jet crashed last week, two months after he and his Wagner mercenaries staged a mutiny against Putin's military.
In a resurfaced clip from April, Prigozhin spoke of being killed and specifically mentioned: "the plane will fall apart in the air."
Days after he had been presumed dead, Russia finally confirmed the Wagner leader's demise.
The crash of Yevgeny Prigozhin's plane joins a chain of violent events, whose traces lead to one place - the Kremlin.
The decree ordering Wagner fighters to swear allegiance to Russia went into immediate effect on Friday.
Belarusian President Alexander Lukashenko said he warned Wagner chief Yevgeny Prigozhin that his life may be in danger.
The Kremlin also said it was impossible to say whether Russian President Vladimir Putin would attend the funeral of Wagner mercenary boss Yevgeny Prigozhin.
The fate of the complex, lucrative web of military and commercial operations that Prigozhin and Wagner created hangs in the balance.
Investigators have opened a probe into the crash, but have not officially confirmed the identities of the bodies recovered from the wreckage.
The Federal Security Service is Russia's primary security agency. It is Russia's successor to the KGB of the Soviet Union.