Tom Cruise had a major request. He wanted IMAX to show his latest “Mission: Impossible” movie — and only his movie — on its giant screens for three weeks. It is the kind of exclusive run that few films get.

So Mr. Cruise went straight to the top. He reached out to IMAX’s chief executive, Rich Gelfond, who had some requests of his own. He wanted all the “Mission: Impossible” premieres, along with press screenings and influencer screenings, to be held at an IMAX theater. And he wanted Mr. Cruise to endorse the company’s screens during his global press tour for the film, which opens this weekend.

“As a joke I said, ‘Tom, no matter what question the press asks you, you’ve got to answer IMAX.’ ‘What’s your favorite scene?’ ‘IMAX,’” Mr. Gelfond, 69, said in an interview. “He agreed to do that.”

In order to get something from IMAX these days, even Hollywood’s top power players have to give some, too.

As movie theater audiences wane and at-home streaming audiences grow, IMAX increasingly stands out as a bright spot in the theater business. The company, founded in Toronto, aims to give moviegoers a more immersive experience with larger screens, better sound and steeper seating, which brings viewers closer to the screen. It now has 416 locations in North America and 1,322 overseas. That is only 1 percent of all the screens in the world, but they often account for a larger percentage of a movie’s box office return, drawing significant crowds for a more expensive ticket than a typical theater seat.

In the past two months, IMAX screens delivered $39 million to the global box office for “Sinners” (out of $321 million total), $30.6 million for “A Minecraft Movie” ($930.1 million total) and $30.5 million for “Thunderbolts*” ($330 million total). (“Thunderbolts*” and “Minecraft” each played in IMAX theaters for two weeks. “Sinners” was brought back to nine locations for a third week.)

As a result, Hollywood studios are putting more emphasis on the IMAX brand, even making the IMAX logo in larger type than the title of the movie in some marketing materials. Disney started this last year with “Kingdom of the Planet of the Apes” and “Alien: Romulus.” For “The Amateur,” a small action movie made by 20th Century Studios this year, the tagline “Vengeance is bigger in IMAX” appeared larger than the movie title. Marvel’s “Thunderbolts*” received similar treatment.

“For some of these movies that have a franchise history — and are also available at home — the IMAX brand can help speak to the big-screen-worthiness of a film and the spectacle,” said Asad Ayaz, the president of marketing at Disney, which owns Marvel and 20th Century Studios. “It differentiates it from streaming, which is also a big business for us, so it can be helpful.”

Yet not everyone in the movie business is thrilled with IMAX’s ascension. Some worry that its limited number of screens, and higher prices for admission, could turn moviegoing from a frequent activity into a luxury experience that further reduces overall attendance.

“It’s great to be able to provide premium experiences to people who want it,” said Greg Marcus, chief executive of the company that operates Marcus Theaters, the fourth-largest chain in the country, but with only three IMAX screens. “But 80 to 85 percent of our business is coming from traditional theaters. And so you have to be very careful to not put down the traditional experience in promoting the other.”

Complicating matters further, most theater chains have their own large-format screens. Regal Cinemas has RPX. Cinemark Theaters has CinemarkXD, and Marcus has both UltraScreenDLX and SuperScreenDLX. AMC, the largest theatrical exhibitor, has several: Dolby Cinema, Prime and Laser.

When a moviegoer buys a ticket to the majority of these large format screens, the exhibitor traditionally evenly splits the revenue with the studio. But when a moviegoer buys a ticket to an IMAX theater, the exhibitor and the studio must give a cut of their shares, often up to 12.5 percent, to IMAX. (Theaters also have to pay a yearly fee to IMAX for the upkeep of their projectors and screens.)

Yet IMAX is the premium large-format option the studios promote more than the others.

“Theaters are struggling, and what seems to really make a different to audiences is the premium format,” said Jeff Goldstein, the president of distribution for Warner Bros. “Each individual exhibitor doesn’t want to give up their brand, and I think their strategy is smart. Any way that brings audiences out for movie going is good, and I think IMAX leads that.”

Mr. Gelfond bought IMAX in 1994 through an investment company he co-founded. At the time, IMAX was primarily known for theaters inside museums and other cultural institutions, showing what he calls “bears, whales and seals” films. It was not until 2003 that the company ventured into partnerships with Hollywood. When “Avatar” was released in 2009, it grossed $250 million on 282 IMAX screens. Hollywood noticed.

IMAX expects to generate $1.2 billion in box office revenue this year, its most ever. But the company is still relatively small. It reported $87 million in revenue last quarter, and $8 million in profit. The majority of the company’s screens are operated by other theater owners as a joint venture, and they share revenue for ticket sales. In those cases, IMAX receives a cut of the box office only from the studios and not the exhibitors, yet it still controls the programming.

The fact that IMAX works with theater chains does not stop Mr. Gelfond from insulting them. “Their premium screens are just regular screens that are just bigger,” he said. “We are investing in a great experience. They are investing in buying a standard projector and putting it on a bigger screen.”

Not everyone agrees with Mr. Gelfond’s assessment about his competitors, including his competitors themselves. Yet his pugilistic style has gotten him far in Hollywood. Recently, he waded into the thorny world of Netflix and theatrical distribution. The entertainment giant has long eschewed releasing movies in theaters before its streaming service. Last month, Ted Sarandos, Netflix’s co-chief executive, called the communal experience of watching a movie in a theater “an outmoded idea.”

But IMAX reached a deal to show Greta Gerwig’s upcoming adaptation of “The Chronicles of Narnia,” a Netflix film, for two weeks in fall 2026 before it goes on the streaming service. That has left some industry insiders wondering whether theaters would be willing to play a Netflix film at all, even if they are contractually obligated to under their deal with IMAX.

“It does cause a conflict in the sense that Netflix has been quite public with negative comments,” Adam Aron, AMC’s chief executive, said in an interview. “But to support Rich we are going to play ‘Narnia.’ And we’d love to be able to convince Ted Sarandos that Netflix would be advantaged if it embraced movie theaters.”

Some say Mr. Gelfond’s direct relationships with some top Hollywood directors have often put him ahead of the studios when it comes to knowing filmmakers’ intentions. Christopher Nolan (“Oppenheimer”) and Ryan Coogler (“Sinners”), both of whom have shot with IMAX cameras, and others have become evangelists for the brand. At the Cannes Film Festival this month, Mr. Gelfond revealed that Mr. Nolan would film the entirety of his next movie, “The Odyssey,” with IMAX cameras.

His connections with some movie stars can help, too — and he’s happy to boast about them. Mr. Gelfond was quick to pull out his phone to share his text exchange with Mr. Cruise moments after the actor rappelled into the stadium at the closing ceremony of the Paris Olympics last summer.

“Beyond awesome!! You’re the best,” Mr. Gelfond messaged the actor. A minute later, Mr. Cruise responded: “Thank you, my friend. We are going to crush it next summer.”