Christian Horner has threatened Mercedes and Ferrari with potential legal action for what he claims to be "defamatory" comments in alleging a breach of F1's budget cap.
Two teams are reported to have spent beyond the prescribed limits last year, with one said to be a minor transgression, and the other a major overspend.
Red Bull and Aston Martin are the teams linked, leading the FIA to issue a statement on Friday noting the "significant and unsubstantiated speculation and conjecture in relation to this matter" while confirming the "assessment is ongoing".
Asked if he had been surprised by comments from Ferrari and Mercedes, Red Bull's direct rivals over the last two years, Horner was critical.
"We were a little bit taken aback by comments that were coming from two of our rival teams yesterday," said Horner.
"The submission between the team [Red Bull] and the FIA is one that is confidential.
"I have no idea what the outcome of our rival's submissions are, or the accounting treatment, or so on, so I would be intrigued to know where their source of information for these fictitious claims have come from.
"They are hugely defamatory and we take umbrage to them.
"One can only assume that it's not coincidental that this is at a point where Max [Verstappen] has his first strike [this season] at a world championship.
"And how on earth do they have this information? Where do they have this knowledge? The FIA have even stated that they haven't even completed their process.
"So unless there is a clear withdrawal of those statements, we will be taking it incredibly seriously and looking at what the options available to us are.
"Because it is absolutely unacceptable to be making comments of the type that were made yesterday that are totally defamatory to the team, to the brands and even to Formula 1.
"And I would be intrigued to know where their source of information has come from."
Red Bull penalty talk "bang out of order"
The FIA deliberately elected not to disclose what sanctions could be applied should a team be found in breach of the cost cap when setting the regulations.
This move was in order to prevent teams from weighing up the risk versus reward of overspending.
Both Ferrari and Mercedes have called for a "severe" punishment for any team found to have broken the rules.
"It is, of course, a process and one that this administration of the FIA has inherited and they are looking to do the very best job that they can," added Horner.
"But I just reiterate, what is totally unacceptable is for teams that are not party to any form of the submission to be making claims about our submission, about perspective penalties.
"It's just bang out of order."
But then making disparaging remarks of his own, Horner added: "Perhaps, when these accusations are made, people in glasshouses shouldn't throw stones.
"I think it's an underhand tactic deployed to detract from perhaps a lack of performance on track this year.
"And, of course, when references are made to last year, this year, next year, we're going to take this extremely seriously.
"So this is an issue for the FIA to deal with, but also an issue for Red Bull to consider what our position is with those comments that have been made."