ISTANBUL — Turkish jets bombed the Syrian Kurdish enclave of Afrin on Saturday as President Recep Tayyip Erdogan of Turkey vowed to crush Kurdish militant forces across northern Syria to remove what he said was a terrorist threat.

The Turkish news agency Anadolu reported that jets bombed more than 100 targets, including an air base, in the first day of air operations against Kurdish militias. Fighters of the Turkish-backed Free Syrian Army also crossed the border into the enclave and engaged Kurdish militants, the agency reported.

Mr. Erdogan has pressed ahead with the offensive despite warnings from the United States that it would further destabilize war-torn Syria. Syria and Russia expressed milder objections.

The Turkish president said “no one can say a word” about the operation.

“Beginning from the west, step by step, we will annihilate the terror corridor up to the Iraqi border,” Mr. Erdogan told a local congress of his Justice and Development Party in the city of Kutahya on Saturday.