WASHINGTON — The Islamic State in Iraq and Syria cannot be defeated unless the United States or its partners take on the Sunni militants in Syria, the chairman of the Joint Chiefs of Staff said Thursday.

“This is an organization that has an apocalyptic end-of-days strategic vision that will eventually have to be defeated,” said the chairman, Gen. Martin E. Dempsey, in his most expansive public remarks on the crisis since American airstrikes began in Iraq. “Can they be defeated without addressing that part of the organization that resides in Syria? The answer is no.”

But General Dempsey and Defense Secretary Chuck Hagel, who both spoke at a Pentagon news conference, gave no indication that President Obama was about to approve airstrikes in Syria.

General Dempsey also was circumspect in describing the sort of broad effort that would be required to roll back ISIS in Syria and Iraq.