In November 2015, a cartoon in Al-Ahram, an Egyptian state-owned newspaper, depicted an Islamic State ogre with “Made in America” emblazoned on his back. It wasn’t unusual. A look at Middle Eastern news media shows that this idea is startlingly common. Even prominent officials in the region, from Egypt’s former culture minister to a former deputy prime minister of Iraq, have publicly ventured conspiracy theories that Washington created the Islamic State.

Enter Donald J. Trump. Last week, Mr. Trump repeatedly claimed that President Obama is “the founder of ISIS.” Even when a sympathetic conservative radio host offered Mr. Trump a chance to backtrack from his ridiculous claim and instead blame the Obama administration’s policies for the Islamic State’s rise, the Republican candidate doubled down: “No, I meant he’s the founder of ISIS. I do.” (The next day, Mr. Trump belatedly took to Twitter to plead sarcasm.)

This will most likely fade from the news cycle as Mr. Trump moves on and the next controversy arises. But these misleading words will reverberate far beyond America’s shores for years to come, and there will be serious implications for American foreign policy.