Qualcomm Inc. said Thursday that it rejected an offer from rival Broadcom Corp. to settle a high-stakes patent dispute over cell phone technology, claiming the proposed deal would cost it up to $2 billion.

Qualcomm suffered a setback June 7 when the U.S. International Trade Commission ruled in the dispute by banning imports of many advanced phones that carry Qualcomm chips starting in August, posing potentially severe headaches for many carriers and handset makers.