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 security pact between Turkey and other NATO members.

The latest moves come amid differences between Ankara and Washington over Syria and a sharp disagreement over the role of Kurdish fighters, who U.S. officials say have played a major role in battling Islamic State militants but who Turkey sees as a terrorist force.

Some U.S. officials and analysts have said the Russian-Turkish deal could jeopardize the future of U.S.-Turkish relations, and raises questions about Turkey’s long-term role in NATO as Russia attempts to expand its own influence in the country in a broader bid to weaken the alliance.

The Pentagon is concerned that the radar capabilities of the S-400 could be used by the Russians to gather intelligence about the stealthy F-35s if the jets were delivered to Turkey.