Although he had been out of sight for three days, he assured Americans he was on top of the situation. “We will not rest until we find all who were involved and hold them accountable,” Mr. Obama said. “This was a serious reminder of the dangers that we face and the nature of those who threaten our homeland.”

Image Air passengers in Pittsburgh on Monday were lined up to undergo tougher security screening. Credit... Jewel Samad/Agence France-Presse — Getty Images

The president spoke hours after Ms. Napolitano tried to clarify the statement she made on Sunday television talk shows that the nation’s aviation security system had worked properly.

Ms. Napolitano said that her remark had been taken out of context and that the attempted attack in fact represented a failure of the security system. “Our system did not work in this instance,” she said on NBC’s “Today” show. “No one is happy or satisfied with that.”

In one of her Sunday appearances, Ms. Napolitano had said the system worked once the attempted bombing occurred, meaning that the government responded by increasing security and alerting other planes.

But on another show, she did not make clear she was referring only to what happened after the incident, making it sound as if the system as a whole worked  an incongruous conclusion given that the suspect was allowed to fly to the United States on a valid visa without extra screening even though he was listed in a terrorism database, his ticket was bought with cash and he checked no luggage.

Administration officials said that during a weekend conference call they had resolved to use the Sunday shows to reassure the public, but that the “system worked” formulation was not in written talking points. “Clearly she could have been more clear, and I think she was today,” said one administration official, who declined to be identified discussing internal strategy.