Apple Music has surpassed Spotify Technology SA in paid U.S. subscriptions, according to people familiar with the matter, in a shift that escalates the music rivals’ contest for listeners world-wide.

Apple Inc.’s streaming-music service has been adding subscribers in the world’s biggest music market more rapidly than its Swedish rival—a monthly growth rate of about 2.6% to 3%, compared with 1.5% to 2% for Spotify—the people said.

Apple Music had more than 28 million subscribers in the U.S. as of February, compared with Spotify’s 26 million, the people said. Neither service publicly breaks out regional subscriber counts, and those figures include only paying users, excluding those in trial offerings that the companies can count in their public subscriber disclosures. Including nonpaying listeners of its ad-supported tier, who generate a fraction of the revenue subscribers do, Spotify has more users overall in the U.S.

Apple was expected to reach its milestone more than six months ago, but Spotify intensified efforts to maintain its lead, expanding various promotions including a discounted subscription bundle with video-streaming service Hulu. More recently, the Swedish company filed an antitrust complaint in Europe claiming Apple abuses its control over the App Store to advantage the iPhone maker’s service, something Apple denies.

Dow Jones & Co., publisher of The Wall Street Journal, has a commercial agreement to supply news through Apple services. Meanwhile, Spotify said in February that it agreed to buy podcaster Gimlet Media, with which The Wall Street Journal also has a content partnership.