LOS ANGELES — In a sign of just how much streaming is changing Hollywood, movie fans will soon be able to rent and buy films for viewing at home — from a movie theater chain.

AMC Entertainment, the largest multiplex operator in the world, will introduce an iTunes-style online video store in the United States on Tuesday, said Adam Aron, AMC’s president and chief executive. The service, AMC Theaters On Demand, will offer about 2,000 films for sale or rent after their theatrical runs, just as iTunes, Amazon and other video-on-demand retailers do.

The movie theater industry has long been at odds with online video. Why trek to theaters if thousands of movies are available at the click of a button at home or on your phone? Sure, new films do not arrive on V.O.D. until they have played in theaters for an exclusive period of about 90 days. But that “windowing” practice, many analysts believe, will become untenable as streaming services like Netflix gain clout.

Hollywood’s five biggest movie studios — Disney, Warner Bros., Universal, Sony and Paramount — have made deals with AMC for catalog and new-release movies. Although DVDs still account for billions of dollars in sales for studios, more profit now comes from digital downloads and rentals.

“For us, it’s all upside,” said Ron Sanders, president of worldwide distribution and home entertainment at Warner. “Most of our other big digital partners are focused on multiple categories — music, books. The great thing about AMC is that movies are the whole focus.”

Films will cost roughly $3 to $5.99 to rent and $9.99 to $19.99 to buy.

Mr. Aron, who took over AMC in early 2016 after running the Starwood hotel chain, has been more willing to embrace change than many other theater executives, in part because he is not blind to his industry’s challenges. Moviegoing in North America — across the chains — has been roughly flat for years, leaving theaters to scratch for growth by charging more for tickets and concessions, a strategy that has its limits.

“Our theater business is mature,” Mr. Aron said. “There is a high-growth opportunity in this digital expansion.”

He called home entertainment a “natural” extension of AMC’s core business — one designed to capitalize on the chain’s fast-growing customer loyalty program, AMC Stubs, which covers more than 20 million households. He said the AMC Stubs database gave the company a marketing advantage for movie rentals and downloads.

For instance, AMC Stubs members bought about six million tickets to “The Lion King” over the summer. When “The Lion King” becomes available digitally on Tuesday, “those people will all get a personalized message from AMC saying that they can now enjoy it at home through AMC Theaters On Demand,” said Elizabeth Frank, AMC’s chief content officer.

Some theater chains in other countries already operate on-demand divisions (Cineplex in Canada is one), but AMC is the first major exhibitor in the United States to do so. Mr. Aron said AMC had been working on the service for more than two years. It was close to introducing AMC Theaters On Demand this summer but held off to fine-tune the technology and online store design.

Under Mr. Aron, AMC has worked to make theatergoing more attractive. It aggressively installed advanced Dolby sound and projection systems, extra-wide screens, and La-Z-Boy-style seats. AMC now serves alcohol in hundreds of its theaters. In 2017, Mr. Aron rolled out greatly expanded food menus at more than 600 theaters.

After noting the popularity of MoviePass, the now-defunct movie ticket subscription service, AMC introduced its own (sustainable) version; for one monthly price, AMC Stubs A-List members can see up to three movies a week.

AMC, based in Leawood, Kan., and partly owned by China’s Dalian Wanda Group, became the largest multiplex chain in the world in 2016 after going on a breathtaking shopping spree. It acquired the Carmike chain in the United States and added Odeon in Britain and Nordic Theater Group in Northern Europe. As a result, AMC began carrying significant debt — roughly $4.7 billion, up from $1.8 billion in 2014.

Its debt load and a bumpy box office ride (attendance at AMC in the United States for the first six months of 2019 fell 3.6 percent, to about 127 million people) have made investors wary. The company’s share price was $8.95 at the close of trading on Monday, down from more than $20 a year ago.