The U.S., along with Arab allies, carried out a series of attacks Tuesday on the Islamic State in Syria. Video posted to social media purports to show the aftermath of those airstrikes. (The Washington Post)

IT DIDN’T take long for the Islamic State to exploit the weaknesses in President Obama’s campaign against it. Last week the militants launched an offensive against a Kurdish-populated area of northern Syria — where until this week Mr. Obama had not approved U.S. airstrikes or the supplying of aid to local forces. By Monday, more than 130,000 people had fled across the border to Turkey, and local commanders said they desperately needed help to defend the strategic town of Kobane.

On Monday night, U.S. officials reported that Mr. Obama had authorized airstrikes in Syria, although officials initially declined to specify what targets were being hit. If the airstrikes are a recognition that the United States cannot defeat the Islamic State by fighting it only in Iraq — and leaving it a haven in Syria — they are to be welcomed. As he did in August in Iraq, Mr. Obama would be justified in shaping the campaign to rescue a vulnerable population — in this case the Syrian Kurds.

To be sure, the situation in northern Syria is more complicated than the one Mr. Obama faced around Mount Sinjar in Iraq in August. The area under attack is controlled by the Kurdish Democratic Union Party, which is allied with the Kurdistan Workers’ Party, a rebel group in Turkey known as the PKK. While there is a truce between the PKK and the Turkish government, relations are poor and Ankara has resisted providing support to the Syrian Kurds. On Sunday, Turkey closed portions of its border with Syria, apparently to prevent Kurds from entering Syria to fight the Islamic State.

That counterproductive action was of a piece with Turkey’s questionable response thus far to the Islamic State. The government of Recep Tayyip Erdogan declined to sign a commitment to fight the extremists that had been drawn up by the United States and Arab states, citing the fact that 49 of its diplomats and other citizens were being held hostage by the Islamic State. Those prisoners were released over the weekend under circumstances that Turkish officials refused to explain. But there is no indication that Mr. Erdogan will be more willing than he has been previously to join or openly support military operations in Syria or Iraq.

Turkey’s recalcitrance is one of several holes in Mr. Obama’s strategy. His plan calls for fighting the Islamic State in Syria by training and arming moderate Syrian rebel forces. But the 5,000 fighters the U.S. plan provides for are unlikely to be enough to defeat the militants, even when training is complete a year from now. Administration officials have no answer to the question of how the U.S.-backed force will be protected from the Syrian army and air force of Bashar al-Assad, nor any plan for defeating the Assad regime or for creating a new political order in Syria has been articulated.

The United States will need a concerted and ambitious approach to Syria if Mr. Obama’s announced goal of degrading and destroying the Islamic State is to be realized. Airstrikes alone will not be sufficient, but they are necessary. And if, in the near term, they can save the Syrian Kurds from a situation described as “urgent” and “dire” by their deputy commander in an interview with the BBC on Monday, they will be eminently justifiable.