THE BEHEADING of another American by the Islamic State brought an appropriately harsh condemnation from President Obama, who called it “an act of pure evil.” Such words about the murder of Abdul-Rahman Kassig, also known as Peter Kassig, ought to reinforce the urgency of destroying the terrorist entity before it can further embed itself in Syria and Iraq and commit other atrocities — such as genocide against non-Muslim communities or a direct attack on the United States.

That’s why it was discouraging to hear Mr. Obama simultaneously rule out steps to patch the glaring gaps in his strategy. At a news conference in Australia on Sunday, the president appeared to reject the deployment of U.S. Special Operations forces to the front lines — a move his senior military commanders have publicly said may be necessary — except in extreme circumstances. Mr. Obama cited the Islamic State’s acquisition of a nuclear weapon as an example of what would move him to act.

For the Joint Chiefs of Staff chairman, Gen. Martin Dempsey, and other U.S. commanders, the threshold is considerably lower. Gen. Dempsey said last week that he could recommend the deployment of the forces in any effort to retake the Iraqi city of Mosul or secure the border with Syria. That’s because the U.S. troops could play a crucial role in directing airstrikes against enemy forces as well as in advising Iraqi and allied units on tactics.

Mr. Obama’s former defense secretary Robert Gates appeared to be speaking for the generals when he bluntly said over the weekend that Iraqi forces won’t be able to “seriously degrade” the Islamic State without the Special Operations forces. Mr. Obama “has given them the mission of destroying ISIS,” the Wall Street Journal quoted Mr. Gates as saying. “But when you then deny the military the authorities they require to achieve the objective, you leave them with a great sense of frustration.”

It’s not just the generals who are chafing. U.S. allies in the region, including Turkey and Qatar, are increasingly uncomfortable with Mr. Obama’s strategy of training moderate Syria rebels in the hope that they will fight the Islamic State but doing nothing to weaken the regime of Bashar al-Assad. Both allies and the rebels point out that the Damascus government appears to be benefiting from the U.S. bombing in Syria and has stepped up attacks on the Western-backed forces.

Asked if he was “actively discussing ways to remove” Mr. Assad, Mr. Obama’s response was a blunt “no.” While “we are looking for a political solution eventually within Syria,” he said, “we’re not even close to being at that stage yet.” That message will be greeted with cheers by the Assad clique and its supporters in Iran; it will encourage the regime to believe it can continue its “barrel bomb” and chlorine gas attacks with impunity. It will also probably ensure that the rift between the United States and its allies against the Islamic State continues to widen.

Mr. Obama appears to recognize the severity of the threat posed by the Islamic State and appears to be focused on the job of leading the fight against it. But if he continues to allow his ideological resistance to steps such as the deployment of ground forces to constrain the campaign, he will ensure its failure.