Formula 1's owners have accused the head of motorsport's governing body of making "unacceptable" remarks about the championship's value.
FIA president Mohammed Ben Sulayem on Monday described $20bn (£16.2bn) as an "inflated price tag being put on F1".
A letter sent by F1 and owner Liberty Media to the FIA says the remarks "overstep the bounds of both the FIA's remit and its contractual rights".
It added that the FIA "may be liable" for any damage to Liberty's value.
The letter, sent on Tuesday, which has been seen by BBC Sport, is co-authored by F1's chief legal officer Sacha Woodward Hill and Renee Wilm, who performs the same role for F1's owner Liberty Media.
F1 holds the commercial rights to the category under a 100-year lease agreement signed by the FIA at the start of this century. US group Liberty Media bought F1 in 2017.
The letter constitutes an explosive response to remarks by Ben Sulayem on Twitter on Monday, which came in reaction to a report by Bloomberg that Saudi Arabia's Public Investment Fund (PIF) had tried and failed to buy F1 for that figure.
Ben Sulayem described the valuation as an "alleged inflated price tag" and said: "Any potential buyer is advised to apply common sense, consider the greater good of the sport and come with a clear, sustainable plan - not just a lot of money."
He added: "It is our duty to consider what the future impact will be for promoters in terms of increased hosting fees and other commercial costs [in the event of any such sale]."
The letter from Woodward Hill and Wilm was addressed to the FIA Executive and its World Motorsport Council, the sport's legislative body.
It marks a dramatic escalation in the strained relationship between F1 and the FIA that has been evident during Ben Sulayem's 13-month presidency.
The letter states that under the 100-year contract, F1 has "the exclusive right to exploit the commercial rights in the FIA F1 World Championship".
It adds: "The FIA has given unequivocal undertakings that it will not do anything to prejudice the ownership, management and/or exploitation of those rights."
It says Ben Sulayem's remarks, "made from the FIA president's official social media account, interfere with our rights in an unacceptable manner".
Woodward Hill and Wilm write: "The circumstances in which the FIA would have any role in a change of control of the F1 group are very limited.
"Any suggestion or implication to the contrary, or that any potential purchaser of the F1 business is required to consult with the FIA, is wrong."
The letter adds that any "commenting on the value of a listed entity, especially claiming or implying possession of inside knowledge while doing so, risks causing substantial damage to the shareholders and investors of that entity, not to mention potential exposure to serious regulatory consequences.
"To the degree that these comments damage the value of Liberty Media Corporation, the FIA may be liable as a result."
It concludes that F1 and Liberty "hope and trust that it will not be necessary to address this issue again".
The FIA has declined to comment.