Two retired U.S. commanders say President Obama still does not have a winning strategy for defeating the Islamic State group after three years and billions of dollars invested in the cause.

Retired Gens. James “Mad Dog” Mattis and Anthony Zinni were asked by Time magazine Tuesday to assess the U.S.-led coalition’s efforts against the Islamic State, also known as ISIS or ISIL. Neither man was convinced the president had a winning long-term strategy.

Mr. Mattis, who led U.S. Central Command from 2010 to 2013, told the publication that Mr. Obama’s efforts are “unguided by a sustained policy or sound strategy [and] replete with half-measures.”

Mr. Zinni, who held the position from 1997 to 2000, was even more blunt.

“It’s a bad strategy, it’s the wrong strategy, and maybe I would tell the president that he would be better served to find somebody who believes in it, whoever that idiot may be,” the former four-star general told the magazine.

Army Gen. Joseph Votel, chief of U.S. Central Command, disagreed, saying, “We are really into the heart of the caliphate.”

The magazine noted that Mr. Obama’s anti-Islamic State coalition does have some politically safe statistics — a 15,000-to-1 kill ratio with an estimated 30,000 members destroyed — but that high body counts do not always translate into victory, since the terror organization quickly replenishes its ranks.

Stephen Biddle, a military analyst at the Council on Foreign Relations, said the president needs to worry about “what would come afterward,” should U.S.-trained forces in Iraq and Syria recapture cities like Mosul or Raqqa.

“Stabilization is unlikely without an investment vastly larger than most Americans will support,” Mr. Biddle said.

Mr. Obama recently gave reporters an update on U.S. operations in Iraq and Syria, where roughly 5,000 troops serve as advisors. He said that while the terrorist group will “inevitably be defeated,” the task requires more than “military force alone.”

“The decline of ISIL in Syria and Iraq appears to be causing it to shift to tactics that we’ve seen before; an even greater emphasis on encouraging high profile terrorist attacks, including in the United States,” the president said Aug. 4, Military Times reported.

“So long as their twisted ideology persists and drives people to violence, then groups like ISIL will keep emerging. And the international community will continue to be at risk in getting sucked into the kind of global whack-a-mole, where we’re always reacting to the latest threat or a lone actor,” the president added.

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