If the initial critical reception for writer-director Baz Luhrmann’s “Elvis” has been a little mixed, the Australian filmmaker has already won over his most important audience: Presley’s family. 

On Saturday night at the Guest House at Graceland, for the film’s invite-only Memphis premiere following high-profile early screenings at the Cannes Film Festival and in both London and Australia, three generations of Presley women — former wife Priscilla Presley, daughter Lisa Marie Presley and granddaughter Riley Keough — joined Luhrmann on stage to bestow their approval on the film, arguably the most substantial feature film ever made about one of global culture’s biggest stars. 

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“Elvis” opens wide on Friday, June 24.

“Usually at a premiere, we’re inviting people into a theater,” said Luhrmann, best known for highly stylized previous films such as “Moulin Rouge” and the Leonardo DiCaprio-led recent adaptation of “The Great Gatsby.” 

“But here, we’ve been invited into a home, and it’s a Presley home.”

Lisa Marie was most blunt, and as a result, perhaps most thankful for the film. 

“I really didn’t know what to expect,” she said. “I’ve seen it twice. The first time I was just nervous, gripping the chair, thinking, oh god what is this? How’s that actor going to be? In my life, it’s been one disappointment after the other in terms of actors portraying my father. Bless their hearts. I’m sure they meant well.”

Standing a few feet from star Austin Butler, Lisa Marie said it was hard for her to find the words to express her appreciation for his performance. 

Butler joined co-star Tom Hanks — who plays Elvis’ manager, the notorious “Colonel” Tom Parker — to lead a group of half a dozen cast members who traveled to Memphis for the screening. 

If there’s an aspect of the film that seems to have drawn the most approval of the Presley women — and here they are simpatico with early critical consensus — it’s Butler’s performance in the impossible lead role. 

“Austin Butler is beyond,” said Priscilla of the actor, who got his start as a child performer on Disney series but might be most familiar for playing Manson Family killer Tex Watson in Quentin Tarantino’s recent “Once Upon a Time in Hollywood. 

“He morphed into Elvis. He spent two years studying for it. He’s a true actor, not just someone who looks like Elvis.”

Butler said that taking on the role “felt like climbing Mt. Everest. For one thing, I didn’t know where to start. There are so many books written about him and so much footage. I’ve seen every interview he ever did. I absorbed everything.”

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That included author Peter Guralnick’s landmark two-part Elvis biographies and the more recent “Being Elvis: A Lonely Life,” by Ray Connolly. 

“There are chapters (“Being Elvis”) that told me things about private moments I’d never read in anything else. You’re seeing the man behind the idol,” said Butler. 

At two viewings — three now — Lisa Marie’s got some work to do to catch up with her mother, who noted during a pre-screening press event that it would be her fifth viewing. 

“I did have a lot of trepidation,” Priscilla acknowledged. “It was Baz Luhrmann. I’d loved all his films but I did know that he does things his way.

“I was so fearful when I finally had the privilege of showing it to Priscilla, and then Lisa Marie and Riley,” Luhrmann said. “There was nothing that mattered to me more.” 

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The multiple Oscar-winning Hanks joked in the theater about being responsible for two Memphis films, including the FedEx-themed “Cast Away.” 

Earlier, he talked about taking on Col. Parker, an unusual role not only for the prosthetics and “fat suit” the slender Hanks used to alter his appearance but for being something of a villain. Or maybe it’s complicated. 

“Col. Tom Parker was a carny, pure and simple. You can look at a carny as a sleazy guy who overcharges for soft-serve ice cream and chili dogs or you could look at him as someone who understands that magic lights on the edge of town attract people who want to have a good time,” said Hanks. 

“You have to bow down to some aspect of the business acumen, smarts and toughness the colonel had. Now, did Elvis suffer from the fact that he had a promoter as opposed to artistic management? I think so, without a doubt.”

While local and state film commission representatives were part of the crowd on Saturday night, all of the Memphis locations in the film — Beale Street’s Club Handy, Sam Phillips’ Memphis Recording Service, Lauderdale Courts, Graceland and more — were recreations. 

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“Elvis” was entirely shot in Luhrmann’s native Australia, without even “B” roll from Memphis. But Luhrmann spent significant pre-production in Memphis and the Mid-South. 

“Five years ago to this month, I came here for the first time,” Luhrmann said. “I was here on and off for 18 months, working with the archives staff, meeting people and digitally mapping, because I had to reproduce Graceland.” 

While the Graceland logo joined the film’s on the backdrop at Saturday’s event, the relationship between the two is somewhat informal. Graceland and Elvis Presley Enterprises are not officially partners on the film, though they certainly hope to capitalize on it. 

Luhrmann noted that he didn’t need acceptance or collaboration, but was happy to have both.

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“I would call it totally informal, but totally in-depth,” said close Elvis confidant Jerry Schilling of his participation on the film. (Schilling is also a character.)

“Baz is a very independent filmmaker but at the right times he would make contact. I felt very strongly that Baz was going to make a special film, but you don’t know until you see it. And Priscilla and I wanted to make sure before we got publicly behind it.” 

Schilling has been involved with a lot of Presley projects over the years, including more directly in many, but he thinks Luhrmann’s “Elvis” might be the biggest and best of them all so far.” 

“This is truly a piece of legacy history,” said Schilling.