NEW DELHI—An Apple Inc. manufacturer has completed a trial run of the first-ever iPhones assembled in India, in an important step in the U.S. tech giant’s push into the fast-growing South Asian market.

The manufacturing of Apple’s cheapest iPhone model, the SE, was handled earlier this month by Taiwanese contract manufacturer Wistron Corp., which has an assembling unit in the southern state of Karnataka, a state official with direct knowledge of the matter told The Wall Street Journal.

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