In a post written Friday on her official Facebook page, O'Connor said she was responding to Hall's "laughable threats."
She wrote, "I'm more amused than I've ever dreamed a person could be and look forward very much to how hilarious it will be watching him trying to prove me wrong."
O'Connor reiterated her previous claims, and added, "I do not like Arsenio Hall."
Prince died last month at the age of 57 at his Paisley Park compound in Minnesota.
Hall's lawsuit reads, "Desperate, attention-seeker Sinead O'Connor maliciously published outlandish defamatory lies about comedian Arsenio Hall, falsely accusing him of supplying illegal 'hard drugs' 'over the decades' to...Prince, and of spiking her with drugs once years ago."
His attorneys deny O'Connor's claims in the lawsuit: "The malicious statements made by O'Connor are absolutely false, and O'Connor's heinous accusations that Hall engaged in this criminal conduct are despicable, fabricated lies," the suit adds, which claims O'Connor knew the accusations were false before she posted them on her Facebook page.
As for Prince's alleged drug use, as ABC previously reported, Minneapolis attorney William Mauzy -- who represents prominent California addiction specialist Dr. Howard Kornfeld -- said at a press conference Wednesday that Prince had arranged to meet with Kornfeld the day before the singer died. Minnesota law enforcement officials are looking into this claim.
If true, this would paint a different picture of the late singer: Earlier reports, citing interviews with former employees, maintained that Prince led a strictly clean lifestyle. Reps for the late singer have not commented.