“It’s really about creating that right marketing campaign, right distribution plan for each movie, allowing us to break through the cultural noise and really resonating with customers,” said Matt Newman, one of three executives Ms. Salke has named as film co-chiefs. The others are Julie Rapaport, who will focus on wide-appeal movies, and Ted Hope, who has overseen Amazon’s art films since 2015.

That stance could frustrate multiplex chains, which insist on a 90-day period of exclusivity, worrying that moviegoers will be reluctant to buy tickets if they know they can catch the same film just a few weeks later in their living rooms. AMC and Regal, for instance, have refused to show Netflix’s “Roma” because Netflix offered only 21 days of exclusivity.

Amazon’s first foray into the movie business was Spike Lee’s “Chi-Raq,” a 2015 comedic drama that received strong reviews but did not sell many tickets. Amazon teamed with an established film company, Roadside Attractions, to release it. Amazon and Roadside reteamed the next year and found an art-house hit in the bleak drama “Manchester by the Sea,” which took in $48 million in North America and received six Oscar nominations, winning two, including best actor for Casey Affleck. “The Big Sick,” a comedy released in 2017 in partnership with Lionsgate, collected about $43 million and received an Academy Award nomination for its screenplay.

Not bad for a newbie.

But Amazon’s track record soured as it pushed toward self-distribution. Its first effort was “Wonder Wheel,” which was undoubtedly hurt by renewed scrutiny of allegations that Mr. Allen molested his adopted daughter Dylan Farrow in 1992. Mr. Allen has steadfastly denied the claims and was not charged. Amazon also financed Mr. Allen’s next film, “A Rainy Day in New York,” but has refused to release it, prompting Mr. Allen to sue.

Amazon’s movie operation has recently shown signs of life. Sitting in her office at the historic Culver Studios, which serves as Amazon’s entertainment headquarters, Ms. Salke noted that the company’s most recent film release, “Cold War,” a foreign-language romance, received three Oscar nominations. “Cold War” has sold $3.6 million in tickets, a decent total for a foreign film. “We really think it’ll also do well when it reaches Prime Video,” Ms. Salke said.

When Ms. Salke arrived at Amazon, her first priority was performing triage on the company’s television business. “Transparent,” the studio’s marquee hit at the time, was in disarray because of the departure of its star, Jeffrey Tambor, who was fired after a sexual-harassment investigation. (He maintained his innocence.) Ms. Salke had inherited another hit, “The Marvelous Mrs. Maisel,” from her predecessor, Roy Price, who was ousted after a sexual harassment scandal of his own. But she needed to quickly jump-start the rest of Amazon’s television business to catch up to a fast-moving Netflix, an insurgent Apple and a Disney-powered Hulu.