The Bravo honcho -- who was, along with the network, sued by McSweeney in an explosive lawsuit last week -- fired off a letter to Leah through his attorneys ... and they make it crystal clear that they believe her allegation of cocaine use against Andy is false and defamatory.

His lawyers don't mince words, saying virtually everything she said about Cohen in the lawsuit is baseless and false, but on the cocaine claim specifically they write ... "[W]e demand that you immediately retract and withdraw all allegations relating to Mr. Cohen’s purported 'cocaine use.'" If she doesn't, they say they're taking her to court.

Andy's legal team continues ... "To be clear: these allegations are categorically false. Mr. Cohen never used cocaine with any cast member on any Real Housewives show or with any other Bravo employee. The absence of any reasonable basis to make such allegations is confirmed by your pleading itself."

They point out there are no details included in her allegation here, which they think points to her not knowing anything concrete ... because it's simply not true. Her attorneys say they believe Leah levied this salacious claim against Andy recklessly just to get headlines and potentially a quick payday.

Andy's lawyers end by saying ... "The truth matters. Litigation cannot be used to create fake news. And it cannot be used as a vehicle to spread false and malicious lies, in furtherance of a shakedown. We demand that you issue an immediate public retraction and apologize to Mr. Cohen. Every day you fail to do so only increases the damages suffered by Mr. Cohen."

McSweeney’s attorney, Sarah M. Matz tells TMZ ... "That Andy Cohen had his counsel and PR agents write a threatening letter to give to the press is hardly surprising.  Mr. Cohen is accustomed to using his power in the media to scare and intimidate people like Ms. McSweeney so that they will not speak out. Mr. Cohen’s attempt to discredit and intimidate Ms. McSweeney to deter her from engaging in legally protected activity in Court is exactly the type of retaliation that this lawsuit was brought to address and only is further evidence for Ms. McSweeney. We do not intend to litigate this matter in the press, and if Mr. Cohen wants to address Ms. McSweeney’s claims, we suggest he do so in Court, not in a letter for the press."

A source close to Leah tells TMZ that she's flabbergasted that he wants to keep bringing attention to this in the press, rather than just letting it play out in court.