Apple Inc.’s plan to create a subscription service for news is running into resistance from major publishers over the tech giant’s proposed financial terms, according to people familiar with the situation, complicating an initiative that is part of the company’s efforts to offset slowing iPhone sales.

In its pitch to some news organizations, the Cupertino, Calif., company has said it would keep about half of the subscription revenue from the service, the people said. The service, described by industry executives as a “Netflix...