“If one more person calls this a catfight… I’m not in a fight,” Parker, 53, told Extra on Tuesday.
“I never fought with Kim.“
The actress also set the record straight on rumors that she had sent Cattrall, 62, gifts in an attempt to smooth things over between them.
“I don’t have to send any gifts to Kim because I’ve never done anything,” Parker explained. “She has felt perfectly comfortable to say lots of things — that’s the beauty of living in a democracy — but I have no apologies, meaning, this isn’t a catfight.”
Despite their differences, the actress said she was “grateful” for Cattrall’s dedication to the character of Samantha Jones in the Sex and the City series.
“This is someone who chose to talk about something and myself, I remain grateful for her work and the role she played on and off camera for all the years we spent together,” she said.
As for whether there have been any ongoing discussions of a third Sex and the City film, Parker said she has “not had any.”
“We went as far as we could last time and the studio said, ‘No, we can’t meet those demands,'” she explained. “We were all signed up except for her.”
She added, “What are you going to do, right?”
In February, Parker opened up to PEOPLE’s Editor in Chief Jess Cagle about the controversy surrounding the iconic HBO show after the plug was pulled on a third film.
“I never talked about it, except [to say] that some of us were disappointed [about the movie not happening],” Parker said at the time.
“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,” the mother of three said. “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.”
She added, “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.”
This first appeared on PEOPLE.