Apple Inc. sued Qualcomm Inc. alleging the chip supplier demanded unfair terms for its technology, escalating long-simmering tension between companies at the heart of the global smartphone industry.

The suit, filed Friday in federal district court in the Southern District of California, claims that Qualcomm leveraged its monopoly position as a manufacturer of baseband chips, a critical component used in cellphones, to seek “onerous, unreasonable and costly” terms for patents, and that Qualcomm blocked Apple’s ability to choose...