In the BBC interview with Artem Loskutov last week the activist urged people to attend a demonstration in support of giving the Siberia region more rights within Russia.
Russia's communication regulator blocked access to the interview and told Izvestia it would be forced to block the entire site if the material which Russian authorities view as extremist is not removed.
"We can block that item for good instantly and if we go down that road we can block the entire BBC Russian service website in our country," Izvestia quoted a source within the communications regulator Roskomnadzor as saying.
Roskomnadzor declined to immediately confirm that it may block the BBC Russian service, but its website republished the Izvestia article.
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The regulator considers the BBC interview and others published by Russian media outlets in which Loskutov called people to attend the "March for a Federal Siberia" as "distributing information on preparations for an unsanctioned public gathering under slogans threatening the territorial integrity of the country", according to Izvestia.
The acting head of BBC's Russia service, Artem Liss, said on his blog that in response to a Roskomnadzor request to remove the material considered "extremist" that they had added an introduction to the interview providing more information about Loskutov, including a suggestion on his blog that the rally was half in jest.
As of today afternoon the BBC Russian service's website could still be accessed from Russia.