Christopher Hope tells TMZ an IG Story posted to Lil Tay's official account Tuesday -- which labels him as the perpetrator of the death hoax -- is not only false ... but defamatory, and he warns that this could land in civil court.

He says, "The person who is responsible for that Instagram post, as well as anyone repeating the completely false and libelous accusation within it, are virtually certain to become defendants in a defamation lawsuit."

Hope adds, "Everything stated is 100% false, and I trust that this should be obvious to anyone who knows me or the long history of absurd and untrue statements made by the various people who have controlled the Instagram account."

As far as what exactly the IG post said ... well, you can read it for yourself. It accuses Hope of being racist and abusive toward women -- in addition to being the one who pre-emptively announced her death ... which turned out not to be true.

Frankly, it's hard to decipher what the truth is in this whole Lil Tay saga ... because all of it is so freaking weird. What we know for certain is that Lil Tay's parents have been embroiled in a nasty custody battle for years now -- which her mom recently told us went in her favor.

Attorneys for Tay's mother, Angela Tian, told us their client was happy to regain a lot of control over how to raise their kid ... and all but guaranteed a comeback to showbiz.

The one person we haven't seen or heard from directly in all this ... Lil Tay.