Mikhail Fridman compared comments by the BP boss to the techniques used by Nazi propaganda chief Joseph Goebbels.
His outburst in an interview with a Moscow newspaper followed Sutherland’s comments last week comparing the tycoons to corporate raiders.
TNK-BP is part-owned by the AAR consortium, led by Fridman, the chairman of the venture, and two other billionaires.
AAR has begun legal action against the British oil giant in what analysts see as a battle by the Russians, with Kremlin support, to increase their hold over the business.
A BP spokesman said of the Goebbels remark: “I don’t think a comment like that deserves the dignity of a response.”
Fridman also called for the replacement of the venture’s chief executive, BP man Robert Dudley. BP said TNK-BP was one of the industry’s top performers and had paid $70billion (£35.6billion) in taxes to Russia since 2003.