President Barack Obama's policy of military action to counter the advance of the Islamic State (ISIS or ISIL) in Iraq is gaining public - and international - support. Our allies in Britain, France and even Germany appear increasingly inclined to join, or at least back, that effort.

But carrying it through to a positive conclusion won't be easy.

Still, this week's horrifying news about ISIS' beheading of an American journalist should bolster that shared international resolve. As President Obama said Wednesday, "Today the entire world is appalled by the brutal murder of Jim Foley by the terrorist group ISIL."

The president added: "Let's be clear about ISIL. They have rampaged across cities and villages killing unarmed citizens in cowardly acts of violence."

Thwarting ISIS' momentum as a border-crossing force of fanatical barbarity will require a united front with plainly defined goals. Though U.S. air strikes against ISIS and humanitarian air drops to help Iraqis displaced by it have achieved short-term successes over the last two weeks, the long-term task remains daunting.

Officials in both the U.S. and Britain have repeatedly stressed that they will put "no boots on the ground" in Iraq. Yet nearly a thousand U.S. armed forces personnel are already on the ground there, and more likely will be needed, even if our military action remains limited to air strikes, to train Iraqi troops, including the Kurdish militia.

That's a hard sell in Western democracies still counting the high costs, in blood and treasure, of lengthy operations in Iraq, as well as Afghanistan.

Ultimately, U.S. officials - and the American public - face two uninviting options: 1) allow ISIS to expand its power and reach, or 2) take strong military measures to stop it.

Unfortunately, the administration's lack of clarity on the nature of our new mission in Iraq feeds the perception - among friends and foes alike - of a lack of determination.

When President Obama first announced air strikes against ISIS in Iraq, he said they were being undertaken to protect U.S. personnel there and to support the humanitarian rescue of refugees.

On Monday, announcing that air strikes had helped Iraqis wrest control of the Mosul dam from ISIS, he seemed to add a new mission. He cited "a long-term strategy to turn the tide" against ISIS and pointed out our national security interest in seeing that it "is contained because ultimately it can pose a threat to us."

The president did reiterate Monday that the war against ISIS remains Iraq's to win or lose, and that he is seeking a "viable partner" in a new Baghdad government "that is inclusive, that is credible, that is legitimate, and that can appeal to Sunnis as well as Shias and Kurds."

Then he added, "We're not there yet."

What the president didn't say was how he intends to "contain" ISIS if the new Iraqi government can't get the job done with our air-power help.

This much, though, is obvious: ISIS, in both Syria and Iraq, has committed heinous atrocities, including mass murder, beheadings and crucifixions. Over the last month in Iraq, it has unleashed a particularly savage reign of terror against Yazidis and Christians.

Defeating - or is that merely containing? - such a fanatical enemy demands a forceful response not just by the U.S. and Iraq but by the civilized nations of the world.

It also demands a clear, effective strategy.