BEIRUT—Dozens of State Department officials this week protested against U.S. policy in Syria, signing an internal document that calls for targeted military strikes against the Damascus government and urging regime change as the only way to defeat Islamic State.

The “dissent channel cable” was signed by 51 State Department officers involved with advising on Syria policy in various capacities, according to an official familiar with the document. The Wall Street Journal reviewed a copy of the cable, which repeatedly calls for...