3:15 PM PT -- Famed attorney Marty Singer is representing Jane Doe and he tells us, "We consider [Bari's] cross complaint to be specious."

It's also worth noting ... prosecutors in the UK are still proceeding with a criminal case against Bari for allegedly raping the woman.

A$AP Bari, one of the co-founders of the A$AP Mob, is going after the woman accusing him of sexual assault ... claiming she wove a web of lies to get him to pay up big-time.

According to legal docs obtained by TMZ ... Bari says his accuser only started alleging sexual assault AFTER she lawyered up. A$AP claims on the night of the incident in July 2017, two police officers showed up to the London hotel and interviewed her ... asking if she had been sexually assaulted.

In docs, Bari says the woman -- who's suing as Jane Doe -- told cops she hadn't been sexually assaulted but was worried about a naked video of her leaking onto the Internet. Bari claims Doe was relieved when she saw one of the cops delete the 10-second video Bari recorded. He claims Doe told police, "seeing the video being deleted was like having a weight lifted" off her shoulders.

As for the video that eventually went viral exposing Doe ... Bari claims that video was taken without his knowledge by a third person in the room when Doe hooked up with Bari's assistant. Bari's suing for defamation and civil extortion for allegedly pressuring him into settling.