Nigel tells TMZ ... "To say that I am shocked and saddened by the allegations made against me by Paula Abdul is a wild understatement. For more than two decades, Paula and I have interacted as dear -- and entirely platonic -- friends and colleagues."

He adds, "Yesterday, however, out of the blue, I learned of these claims in the press and I want to be clear: not only are they false, they are deeply offensive to me and to everything I stand for."

NL finishes by saying ... "While Paula’s history of erratic behavior is well known, I can’t pretend to understand exactly why she would file a lawsuit that she must know is untrue. But I can promise that I will fight this appalling smear with everything I have."

Nigel doesn't elaborate on the "erratic behavior" he's referring to -- but it does seem to be a thinly-veiled jab at her alleged affair with ex-'Idol' contestant Corey Clark from way back in the mid-2000s ... which she's always maintained did not happen.

TMZ broke the story ... Paula filed her bombshell suit against Lythgoe Friday, alleging she'd been sexually assaulted by him on at least two occasions -- not to mention allegedly being harassed by him on others.

She claimed that in the early seasons of 'Idol,' Lythgoe grabbed her breasts and genitals in an elevator they were in while out on the road for regional auditions ... this while allegedly tying to kiss her. She also claims he forced himself onto her at some point during her judging stint on 'So You Think You Can Dance' after inviting her to his home to talk shop.

Welp, Nigel is denying all of it ... and says Paula's making the whole thing up. None of the other talent from either show has spoken up on this just publicly ... at least not yet anyway.