WASHINGTON—Elon Musk’s SpaceX is seeking to qualify for federal subsidies to provide broadband service to rural areas, over the objections of competitors who say its satellite-based technology is unproven.

The company, formally known as Space Exploration Technologies Corp., has convinced the Federal Communications Commission to propose a policy change that would improve its chances of winning federal funds to expand internet service in far-flung parts of the U.S., records show.

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