WASHINGTON — President Obama on Tuesday angrily denounced Donald J. Trump for his rhetoric in the aftermath of the shooting massacre in Orlando, Fla., saying the presumptive Republican presidential nominee was peddling a “dangerous” mind-set that recalls the darkest periods in American history.

“We hear language that singles out immigrants and suggests entire religious communities are complicit in violence,” Mr. Obama said at the Treasury Department. His statement came after a meeting with his national security team on the status of the American effort against the Islamic State, which the president said had been dominated by discussion of the Orlando rampage.

“Where does this stop?” the president said of Mr. Trump’s approach, noting that he had proposed a ban on admitting Muslims into the United States, and that the Orlando assailant, like perpetrators of previous domestic terrorist attacks in San Bernardino, Calif., and Fort Hood, Tex., was an American citizen.

“Are we going to start treating all Muslim-Americans differently? Are we going to start subjecting them to special surveillance? Are we going to start discriminating against them because of their faith?” Mr. Obama said, his voice rising during his most direct condemnation yet of Mr. Trump. “Do Republican officials actually agree with this?”

The president, who has steadfastly refused to use the term “radical Islam” to describe the Islamic State, which is also known as ISIS or ISIL, bitterly rejected criticism from Mr. Trump and other Republicans about failing to use the phrase.

“If there’s anyone out there who thinks we’re confused about who our enemies are, that would come as a surprise to the thousands of terrorists who we’ve taken off the battlefield,” Mr. Obama said. “There’s no magic to the phrase ‘radical Islam.’ It’s a political talking point, it’s not a strategy.”

The president said he would not use the wording because he was unwilling to give the Islamic State the victory of accepting their vision of themselves as leaders of a holy war between Islam and the West.

“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,” Mr. Obama said.

Mr. Obama is scheduled to travel to Orlando on Thursday to visit with the surviving victims and the families of those killed in the rampage on Sunday morning

On Tuesday, he called on Congress to enact gun restrictions that it has so far resisted, including the resurrection of a ban on assault weapons and a measure that would bar the ability to purchase guns to those on no-fly lists because of suspected terrorist ties.

“Enough talking about being tough on terrorism,” Mr. Obama said. “Actually be tough on terrorism and stop making it as easy as possible for terrorists to buy assault weapons.”