Sheriff Israel said on Sunday that his deputies arrived four minutes after Mr. Cruz had left the freshman building where the massacre took place. But Mr. Tapper noted that the deputies did not know at that point that Mr. Cruz had already left, and should have proceeded as though the shooting were still underway.

“We will investigate every action of our deputies, of their supervisors,” the sheriff said, adding that Coral Springs police officers will give witness statements to investigators from his office. “If they did things wrong,” he said of his department’s personnel, “I will take care of business in a disciplinary manner.”

Sheriff Israel, who effusively praised his deputies in the immediate aftermath of the shooting, had insisted in a news conference on Wednesday that his deputies had not delayed their entry into the school. He appeared at a town-hall-style event that evening, broadcast on CNN, during which he criticized the National Rifle Association aggressively and urged state lawmakers to give police more power to commit the mentally ill to hospitals involuntarily.

He did not mention Deputy Peterson’s inaction on that broadcast, even though, as he told Mr. Tapper on Sunday, he had seen video footage earlier that day showing that the deputy had stayed outside.

The sheriff said on Sunday that his office waited until Thursday, the day after the broadcast, to corroborate that the deputy had not entered the school and to notify families of the victims about the finding.

“I’m not on a timeline for TV or any news show,” he said.

Sheriff Israel said he has asked the Police Executive Research Forum, based in Washington, to conduct an independent after-action report on how his office responded to the shooting.

He rejected suggestions that his office had missed repeated signs that Mr. Cruz was a threat to Stoneman Douglas High, even though at least 23 calls involving Mr. Cruz were made to deputies over the past decade. The sheriff’s office is investigating how two of those calls were handled, and has placed the two deputies who responded to them on restricted duty.