In a speech on Tuesday to update the nation on the battle against the Islamic State, given against the backdrop of the Orlando, Fla., massacre, President Obama gave the most powerful rebuke yet to the increasingly unreasonable and dangerous ravings of the presumptive Republican presidential nominee, Donald Trump.

Mr. Obama started by listing the ways in which his administration has worked to subdue the threat of terrorism abroad and at home. And because of the use of American and allied force, the Islamic State is losing ground in Syria, Iraq and Libya, he said.

Then he addressed the accusation — a fetishized Republican talking point, repeated by Mr. Trump after Orlando — that Mr. Obama is surrendering to the enemy by avoiding the label “radical Islam.” The idea that reciting those words would help magically defeat the terrorists is absurd, and worse. It plays into the desire of groups like ISIS and Al Qaeda to make the war, as Mr. Obama said, “a war between Islam and America, or between Islam and the West. They want to claim that they are the true leaders of over a billion Muslims around the world who reject their crazy notions.”

Implying that these terrorists speak for Islam aids their propaganda, Mr. Obama said. “That’s how they recruit. And if we fall into the trap of painting all Muslims with a broad brush, and imply that we are at war with an entire religion, then we are doing the terrorists’ work for them.”