In the wake of the terror attacks in Paris, Brussels and beyond, President Barack Obama has recognized the need to accelerate the campaign against the Islamic State before the jihadis strike big again in Europe — or in the United States.

U.S. air strikes have helped Kurdish and Arab fighters take back territory from the Islamic State in Syria and Iraq. But the jihadis are still entrenched in the main centers of their so-called caliphate — Raqqa, Syria, the city where the Islamic State’s senior leaders plot their overseas attacks, and Mosul, Iraq’s second-largest urban area.

“We should no longer tolerate the kinds of positioning that is enabled by them having headquarters in Raqqa and Mosul,” Obama said earlier this month.

Yet the administration is caught up in a debate over which to target first, a decision so fraught that it must be made in the White House.

After a trip last month to the Kurdish regions of Iraq and Syria, I’d argue that the choice is clear: Raqqa first. The city is the seat of Islamic State “caliph” Omar al-Baghdadi. Its loss would smash the Islamic State territorial and religious myths.

Moreover, Raqqa is much smaller than Mosul and less ethnically complex, and there is a Syrian fighting force on the ground that, with American help, holds the potential of taking the city. In Mosul, to the contrary, the Iraqis are far from having enough forces to succeed, and the Iraqi government is in turmoil.

Yet a decision to assault Raqqa is hung up in large part not by resistance from jihadi enemies, but by opposition from Turkey, a (supposed) NATO ally.

How can this be? Because going for Raqqa would require a closer U.S. alliance with the Syrian Kurds, who are loathed by Turkey’s Kurdophobic president.

Kurdish fighters have seized back swaths of Syrian territory from the Islamic State with the help of U.S. air strikes. But the Syrian Kurds’ PYD party is detested by Turkish President Recep Tayyip Erdogan because of its ideological links to the PKK, the Turkish Kurdish rebel movement.

Syrian Kurds, who share a long border with Turkey, have declared their own federal statelet within Syria, and Erdogan fears they will inspire Turkish Kurds.

However, PYD leaders point out that their movement is not at war with Turkey and is not attacking Turks. Moreover, they insist they do not want a united Kurdistan that would link them up with Turkey’s Kurdish region. They say their goal is a federal state within Syria’s current boundaries.

The PYD is eager to have its fighters, joined by local Sunni Arab tribes, push the Islamic State out of towns along the Turkish border, and link up areas the Kurds have already liberated. These towns include Manjib, an Islamic State hotbed that nurtured some of the jihadis who attacked Brussels. These jihadi killers were able to enter and leave Turkey from Syria at will for years — with little effort to stop them by Ankara.

Yet on a recent trip to Washington, Erdogan denounced U.S. cooperation with the Syrian Kurds and called them terrorists. He wants Obama to back Syrian Arab and ethnic Turkmen rebels who are allied with Turkey. Never mind that these groups are painfully small in numbers and have proved hapless when confronting the Islamic State along the Turkish border. Erdogan still insists that America back his guys and stiff the Kurds.

What’s so frustrating is that Ankara was talking to the Syrian Kurds not so long ago. And Erdogan was negotiating with the imprisoned leader of the PKK. But recently, due to Erdogan’s political ambitions and some PKK mistakes, the Turkish-PKK civil war has restarted. Thus domestic Turkish politics are blocking progress in wiping out the Islamic State caliphate.

U.S. officials are humoring Erdogan up to a point — since Turkey is a NATO member and Washington wants to use the Turkish airbase at Incerlik. However, the Pentagon is still helping Syrian Kurdish fighters with air strikes, light arms, and the presence of 50 U.S. special forces in Syria. That number could increase.

Sooner rather than later, the White House must clarify to Erdogan that his Kurdo-phobia is thwarting the campaign against the Islamic State. U.S. officials might recall that when U.S. planes helped Syrian Kurds retake the border town of Kobbani from the Islamic State, in the face of Erdogan’s outrage, the Turkish leader caved in.

However, there is another obstacle to the liberation of Raqqa that U.S. forces are working to address: the need to substantially increase the numbers of Sunni Arabs who are fighting with the Kurds in an umbrella force known as the Syrian Democratic Forces. This is critically important because Raqqa and nearby small towns have a heavy population of Sunni Arabs and would be fearful of an operation that was spearheaded predominantly by Kurds. And Sunni forces will be needed to police Raqqa after the Islamic State is gone.

However, if Sunnis are convinced an operation to liberate Raqqa is on the way, firmly backed by Washington and its allies, those tribal fighters are much more likely to materialize. It’s time to make that commitment, and to make clear to Erdogan that he can’t stand in the way of the fight to end the caliphate.

The message to Ankara must be clear: There is no way to liberate Raqqa without full participation of the Syrian Kurds. And the operation to liberate Raqqa needs to start soon.

Trudy Rubin is a columnist with the Philadelphia Inquirer.