Levin - who wrote a biography of Prince Harry in 2018 - claimed the TalkTV presenter had an "agenda to attack me" after she was confronted to provide factual evidence to back up her opinions of the Duchess of Sussex.
Levin said: "The Prince Harry I knew was absolutely charming, instinctive like his mother, full of fun, and now he looks when he's out - incredible unhappy and very, very tense and resentful."
Feltz replied: "I wonder if you're just rehashing that kind of biblical story that we've all heard so many times of the evil temptress and the trusting and vulnerable man who is gullible and mailable in her hands. And I wonder whether it's based on any kind of real knowledge of her personality and what she truly feels and thinks, because after all - how can you know?
“It’s a question about what you base your thoughts on - whether you’ve just imagined it, whether you’re projecting, whether you really know, whether they're facts, whether it's conjecture. You say what you think but what are the thoughts based on?”
Levin said: "I'd rather you didn't attack me, if you want to attack me you shouldn't invite me on. You're not just asking, you've got an agenda there to attack me."
Feltz then pointed out that Levin had tweeted about unfounded rumours that Markle had planned to invite US TV cameras to follow her on a walk-about greeting grieving members of the British public following Queen Elizabeth's death, and this had prompted Prince William to invite her and Prince Harry to join him and the Princess of Wales.
Feltz said: "Apparently there's no factual evidence at all, if you're going to tell me that there is that's fine."
Levin said: "I don't have to tell you anything, I don't really want to be invited onto this programme and treated in this manner. I'm not going to let you interview me again."
Feltz has been a frequent critic of Markle, most recently of her speech at the One Young World summit in Manchester.
Feltz said: "She doesn't come across all that sincere and I just thought she should have been like 'well enough about me let's talk about you' or equality, diversity, world peace or any of the very important topics we're shining a light on."
But she did defend her when the Duchess said she had been the subject of racist abuse.
The broadcaster said on This Morning last year: "If Meghan feels that she was subject to racism, then it's not for us to disagree - only she knows how she felt.
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"I'm a Jewish woman and I would not appreciate it if I said I had been subject to anti-semitism and somebody else tried to tell me I hadn't."