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MUNICH — Just hours after Reed Hastings announced this month that Netflix, the video-streaming service that he co-founded, would become available in 190 countries, he got an unexpected surprise.

Along with new customers in large markets like India and Russia, Mr. Hastings said, people on Réunion Island — a small French-governed island off the coast of Madagascar — were some of the first to sign up as new subscribers, making them maybe the most unlikely people to try Netflix’s fast-expanding global service.

“They must have pretty good Internet connections,” Mr. Hastings joked in an interview here on Sunday at DLD, a technology and media conference. “We saw a lot of people signing up there.”

Fulfilling the needs of these new customers — in out-of-the-way places like Réunion Island, along with more populous countries like Indonesia — is now a top priority for Mr. Hastings, whose goal is to turn Netflix into a global media giant.

That involves signing deals for local-language content in many of the countries where Netflix has just arrived, funding new programming in Japanese and other languages and offering subtitles for non-English speakers who want to get their fix of “Orange Is the New Black” or “House of Cards,” two of the company’s popular American shows.

“We have a lot of work to do to add more languages,” Mr. Hastings said, adding that the company would add roughly a couple of new languages a year as part of its global introduction. In many of the 190 countries where Netflix is now available — including Turkey and Poland — the service is available in English, but not the local language.

“We’re seeing sign-ups in places like Somalia,” he said. “It’s incredible to see.” That shows, he added, “how the Internet is truly global.”

Despite his lofty global ambitions, Mr. Hastings still has his work cut out to persuade people, particularly in developing countries, to spend roughly $7.50 a month for the video-on-demand service, a price that may prove too high for many potential subscribers.

Netflix must also overcome a growing number of local rivals, many of which have mimicked the company’s business model to offer subscription on-demand programming, often in national languages, to quench people’s thirst for content obtained over the Internet.

On Sunday, Mr. Hastings remained upbeat about the challenges ahead. Netflix, he said, was not just competing with other video-on-demand services, but it also wanted to grab a few hours of people’s days when they could be watching television, reading a book or even sharing a glass of wine with friends.

“If we try to outdo local competitors, we can differentiate ourselves for our customers,” Mr. Hastings said. “We don’t have to win everyone’s viewing habits. We only have to win a few hours of people’s time.”