The 52-year-old actor was publicly called out by Cattrall for not being "nice" enough on the sets of the hit show and subsequent films over the last few months.
The actor, who famously played Samantha Jones on the HBO series, had appeared on "Piers Morgan's Life Stories" last year and said she was not friends with her "SATC" co-stars.
"I never talked about it, except that some of us were disappointed. But I never responded to the conversation Kim had with Piers Morgan, where she said things that were really hurtful about me. We had this experience and it was amazing, and nothing will ever be like it," Parker told People magazine .
Parker, however, added, "We had a connection with an audience, and we had a connection with the city and with this crew, and we got to tell these crazy stories with each other. So I don't want to mess with that.
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"I couldn't imagine anyone else playing that part. So there was no fight; it was completely fabricated, because I actually never responded. And I won't, because she needed to say what she needed to say, and that is her privilege."
Parker has not responded to Cattrall's accusations.
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