ISTANBUL (Reuters) - The Trump administration is starting to repair ties with NATO ally Turkey, U.S. Secretary of State Rex Tillerson said on Monday, without acknowledging Washington still pursued some policies that have been the focus of tension.

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Tillerson’s comments came a day after he met Turkish President Tayyip Erdogan for talks on regional security issues, including U.S. backing for Kurdish Syrian YPG forces fighting to drive Islamic State from their Raqqa stronghold.

“I think we’re beginning to rebuild some of that trust that we lost in one another. They lost our trust to a certain extent, we lost theirs,” Tillerson, in Istanbul for an international petroleum conference, told U.S. consulate staff members.

Turkey views the YPG as a branch of the PKK, the outlawed Kurdish separatist group that has been waging an insurgency in southeastern Turkey since the 1980s. It fears an effort to form a contiguous Kurdish state embracing some Turkish territory.

Ankara was infuriated last month when Washington – which has designated the PKK a terrorist group - announced that it would continue the Obama administration’s policy of arming the YPG, although U.S. officials insist that the United States will retrieve the weapons once Islamic State is defeated.

The Trump administration also has persisted in resisting Turkey’s demand that it extradite Fethullah Gulen, an Islamic cleric who lives in Pennsylvania and is accused by Erdogan of masterminding a failed military coup in July 2016.

A decision by U.S. prosecutors last month to charge a dozen Turkish security and police officers after an attack on protesters during Erdogan’s visit to Washington also angered Ankara.

STRATEGIC LOCATION

Tillerson made no mention of the continuing disagreements. He said that since becoming Secretary of State he had met Erdogan three times “and I think each meeting things are getting a little better in terms of the tone between us”.

The U.S. relationship with Turkey is “extraordinarily important from a security standpoint to the future economic opportunities,” he said, noting the country’s strategic location at the crossroads of Europe and the Middle East.

“(This) is why we must put the relationship on the mend... and I think we’re taking the first steps in that regard.”

Muslim-majority Turkey has NATO’s second-largest standing military and its Incirlik Air Base is critical to U.S. military operations in the Middle East, serving as the base from which the U.S.-led coalition has been staging strikes in support of the offensive being waged against Islamic State in Raqqa by the YPG and Syrian Arab fighters backed by U.S. troops.

“We’re making some progress down in Syria. We’re hopeful that we can replicate that with Turkey, on some areas in the north part of Syria.

Tillerson’s comments, however, sharply contrasted with comments by Erdogan two weeks ago, when he harshly criticized the arming of the YPG by the United States.

“The ones who think they are tricking Turkey by saying they are going to get back the weapons that are being given to this terrorist organization will realize that they are making a mistake eventually,” he told members of his ruling AK Party.

“But it will be too late for them,” he added, saying that if violence spilled over Syria’s border into Turkey, Ankara would hold to account anyone who supplied arms to the YPG.