WASHINGTON—President Trump said the U.S. would withhold sales of advanced F-35 stealth jet fighters to Turkey after Ankara received a new air-defense system from Russia, putting new strains on the North Atlantic Treaty Organization.

The decision to cancel the F-35 shipment was expected, but until Mr. Trump’s remarks on Tuesday, the administration had held off on responding to Turkey’s decision to accept delivery of the Russian S-400 system. Turkey’s action and the U.S. response inject tension and uncertainty into the 67-year...