SUNRISE, Fla. — A day after remarks that appeared to suggest that gun rights advocates harm Hillary Clinton, Donald J. Trump sprayed his fire at President Obama on Wednesday, accusing him of creating the Islamic State and saying the terrorist group “honors” him.

“In many respects, you know, they honor President Obama,” Mr. Trump told a raucous and rowdy crowd in Florida on Wednesday night. “He’s the founder of ISIS. He’s the founder of ISIS. He’s the founder. He founded ISIS.” He added, “I would say the co-founder would be crooked Hillary Clinton.” During an extended riff on the crisis in Crimea, Mr. Trump added extra emphasis on the president’s full name, saying that it occurred “during the administration of Barack Hussein Obama.”

Mr. Trump’s statement was an escalation in his recent criticism of the Obama administration’s handling of the terror threat, as he had previously accused only Mrs. Clinton of having a “founding” role in the terror group. His suggestion that the president was honored by ISIS recalled an earlier controversy when Mr. Trump seemingly implied that the president had some connection to the terrorist massacre of 49 people at the Pulse nightclub in Orlando.

“He doesn’t get it, or he gets it better than anybody understands,” Mr. Trump told Fox News in June. And the use of the president’s middle name recalled Mr. Trump’s questioning of Mr. Obama’s faith during his crusade several years ago to prove that Mr. Obama, who is Christian, was not born in the United States.