BEIJING—As Apple Inc. grapples with falling iPhone sales this year, it is pushing to cut better deals for parts with its suppliers, while carriers in the crucial China market have mobilized to push iPhone sales with deep discounts.

In recent months, Apple suppliers say the Cupertino, Calif., company has told them to accept price cuts for parts destined for the next-generation iPhone while cutting forecasts for order volume. This is likely to hurt some suppliers’ earnings in the second half of the year.

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