Wilde directed and costars in Don't Worry Darling, a psychological thriller in which Pugh plays Alice, a housewife in the seemingly perfect community of Victory who begins to see through the facade as her husband Jack (Harry Styles) gets in deeper.
At the film's Venice Film Festival premiere on Monday, Wilde, 38, and Pugh, 26, posed with costars Styles, Gemma Chan, Sydney Chandler, Chris Pine and Nick Kroll on the red carpet. Pugh brought her grandmother along for the red carpet debut.
The photo op came hours after Pugh sat out the film's press conference while on a flight from the Dune: Part Two set and Wilde fielded a question about rumors of a "falling out" between herself and Pugh.
Wilde responded to the question, "Florence is a force, and we are so grateful that she's able to make it tonight despite being in production on Dune. I know, as a director, how disruptive it is to lose an actor even for a day, so I'm very grateful to her, to Denis Villeneuve for helping us. And we're really thrilled we'll get to celebrate her work tonight. I can't say enough how honored I am to have her as our lead. She's amazing in the film."
"As for all the endless tabloid gossip and all the noise out there, I mean, the internet feeds itself," she continued. "I don't feel the need to contribute. It's sufficiently well nourished."
The panel's moderator then skipped over a question about Shia LaBeouf, following a leaked video that Wilde allegedly sent to LaBeouf went viral on social media and he claimed he quit the movie and wasn't fired by her.
In the clip, Wilde — who has claimed she fired LaBeouf from Don't Worry Darling to preserve a non-aggressive atmosphere on set — asked LaBeouf not to depart the movie. Wilde referred to Pugh as "Miss Flo" in the video and alluded to unresolved tension between Pugh and LaBeouf, 36. (Styles, 28, ultimately replaced him in the role.)
"I feel like I'm not ready to give up on this yet, and I too am heartbroken and I want to figure this out," Wilde said in the video. "You know, I think this might be a bit of a wake-up call for Miss Flo, and I wanna know if you're open to giving this a shot with me, with us. If she really commits, if she really puts her mind and heart into it at this point and if you guys can make peace — and I respect your point of view, I respect hers — but if you guys can do it, what do you think? Is there hope? Will you let me know?"
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There have also been reports of a rumored feud between Wilde and Pugh behind the scenes of the movie. In her Variety cover story last month, however, Wilde praised the "extraordinary" actress and called "tabloid media" a "tool to pit women against one another and to shame them."
"She's clearly the most exciting young actress working today," Wilde said of Pugh, adding that the cast was "brought so close by the bubble of the production."
After the announcement of the film's release, there were reports that claimed Styles, who is currently dating Wilde, was paid three times more than Pugh for the project. Wilde denied that allegation, blaming all false narratives as "clickbait."
She told Variety, "There has been a lot out there that I largely don't pay attention to. But the absurdity of invented clickbait and subsequent reaction regarding a nonexistent pay disparity between our lead and supporting actors really upset me."
Stephane Cardinale - Corbis/Corbis via Getty
"I'm a woman who has been in this business for over 20 years, and it's something that I have fought for myself and others, especially being a director," said Wilde. "There is absolutely no validity to those claims."
Pugh told Harper's Bazaar last month that Don't Worry Darling should get more attention from audiences other than interest in the sex scenes, like some of the online conversation has been focused on since the trailers debuted.
"When it's reduced to your sex scenes, or to watch the most famous man in the world go down on someone, it's not why we do it," she said. "It's not why I'm in this industry."
"Obviously, the nature of hiring the most famous pop star in the world, you're going to have conversations like that," she added. "That's just not what I'm going to be discussing because [this movie is] bigger and better than that. And the people who made it are bigger and better than that."