Tensions between the U.S. and Turkey over Washington’s support for Kurdish fighters in Syria—viewed as terrorists by Ankara—sharpened Tuesday when Turkish officials demanded a meeting with the American ambassador.

The Foreign Ministry summoned U.S. Ambassador John Bass to a meeting in Ankara after the State Department said publicly Monday it doesn’t consider the Syrian Kurds to be terrorists.

Turkey deems the Democratic Union Party, known by its Kurdish acronym PYD, to be a terrorist group as an offshoot of the Turkey-based Kurdistan Workers’ Party, or PKK. While the U.S., like Turkey, classifies the PKK as a terror group, it has lauded the Syrian PYD as an effective organization in countering Islamic State militants.

Tensions over that difference in views have been building for months. On Monday, State Department spokesman John Kirby said at a news briefing in Washington that the U.S. doesn’t consider the PYD to be terrorist.

“We don’t, as you know, recognize the PYD as a terrorist organization. We recognize that the Turks do, and I understand that,” Mr. Kirby said.

The Foreign Ministry called in Mr. Bass after those remarks to express the government’s displeasure, Turkish media reported. The State Department confirmed the meeting took place, but declined to describe the tone or subject of the meeting.

The support the U.S.-led coalition against Islamic State has voiced for the PYD and other groups closely associated with the PKK has been an irritant in the U.S.-Turkey relationship over the past several months.

Turkish President Recep Tayyip Erdogan last week harshly criticized Brett McGurk, a presidential envoy in matters involving Islamic State, for photos showing him with a PYD commander widely believed to be a former member of the PKK.

Mr. Erdogan told reporters on his presidential plane in remarks published last week that the dispute undermined Turkish confidence in the U.S. “How can we trust [you]?” he said. “Is it me that is your partner, or is it the terrorists in Kobani?”

In Washington on Tuesday, Mr. Kirby reaffirmed the U.S. position on both the PYD and PKK, adding officials were talking to Turkish counterparts about their differences.

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