F1 chiefs were responding to a series of tweets from the FIA president on Monday in which he described a £16.2 billion valuation of the sport as "inflated".
But in an explosive letter, composed by F1's legal team, sent to the FIA's World Motor Sport Council, the grid's 10 teams, and leaked to Sky News, Ben Sulayem has been described as "overstepping the bounds of the FIA's remit", and told that the FIA could be "liable" for harming F1's owners' Liberty Media's value.
F1's reaction to Ben Sulayem's social media posts is a dramatic escalation in tensions between the sport and the FIA.
Last week, Bloomberg News reported that Saudi Arabia Public Investment Fund explored the possibility of a $20bn takeover of F1.
American conglomerate Liberty Media ended Bernie Ecclestone's reign when it bought F1 from private equity firm CVC Capital Partners for £6.4bn in 2017.
Ben Sulayem, who has been president of the FIA for 13 months, tweeted: "As the custodians of motorsport, the FIA, as a non-profit organisation, is cautious about alleged inflated price tags of $20bn being put on F1.
"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.
"It is our duty to consider what the future impact will be for promoters in terms of increased hosting fees and other commercial costs, and any adverse impact that it could have on fans."
But his tweets angered F1's hierarchy, provoking the letter - drafted by the sport's legal guru Sacha Woodward Hill and Liberty's legal chief Renee Wilm - to be dispatched to all of the grid's major players.
It read: "Formula One has the exclusive right to exploit the commercial rights in the FIA Formula One World Championship.
"Further, the FIA has given unequivocal undertakings that it will not do anything to prejudice the ownership, management and/or exploitation of those rights.
"We consider that those comments, made from the FIA president's official social media account, interfere with those rights in an unacceptable manner."
The letter continued: "[That] any potential purchaser of the Formula One business is required to consult with the FIA is wrong," and Ben Sulayem had "overstep[ped] the bounds of the FIA's remit".
It added: "Any individual or organisation commenting on the value of a listed entity or its subsidiaries, 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."
Both F1 and the FIA declined to comment when contacted by the PA news agency. The new F1 season starts in Bahrain on March 5.