The United States and Turkey struggled on Thursday to resolve a deep dispute over the Kurdish role in the fight against Islamic State of Iraq and the Levant (ISIL), as US Secretary of State Rex Tillerson wrapped up his first trip to Turkey.

As the US prepares an operation to retake the de facto ISIL capital of Raqqa in Syria, the Turks and Americans are deadlocked over who should do the fighting.

Turkey wants the US to partner with its military and Turkish-backed forces in Syria. But Washington has been backing Syrian Kurdish fighters who have proven the most effective ground force against ISIL.

"Let me be very frank: These are not easy decisions," Tillerson said in Ankara. "They are difficult decisions that have to be made."

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Turkey considers the Kurdish force, known as the YPG, to be a "terrorist group" that threatens Turkey's security.

The US hasn't formally announced a decision on who will be part of the Raqqa operation. But all signs point to Washington continuing to bet on the Kurds. In recent days, the US military airlifted hundreds of Syrian Kurdish forces along with US military advisers and artillery behind enemy lines in preparation for the Raqqa offensive.

Tillerson said he and Turkish Foreign Minister Mevlut Cavusoglu had explored "a number of options and alternatives" for the operation, but signaled they'd reached no agreement.

Cavusoglu, standing alongside Tillerson, warned past US support for Syrian Kurdish forces had already damaged America's relations with Turkey. He accused the US of using one "terrorist organisation" to fight another.

"It has negatively affected the Turkish people's sentiments toward the United States," Cavusoglu said in Turkish.

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Cavusoglu claimed the Trump administration and the US military have accepted that the YPG - the dominant force in the US-backed Syrian Democratic Forces - is intrinsically linked to the PKK, or Kurdistan Workers' Party.

The PKK has led a three-decade long insurgency in southeast Turkey and is considered a "terrorist group" by the US. But the US has not extended that designation to the Kurds in Syria, and American military officials have said there's no evidence the YPG has posed a threat to Turkey in recent years.

"The US military accepts that there is no distinction between the PKK, which is a terrorist organisation, and the YPG. However, the previous administration failed to acknowledge that," said Cavusoglu, referring to Barack Obama's government.

"We have repeatedly expressed that it is a mistake to consider cooperation with a terrorist organisation in the guise of the YPG, and in the long term that would be a mistake in Syria."

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Though the US and Turkey share a goal of defeating ISIL in Iraq and Syria, the US has been concerned that Turkey's Operation Euphrates Shield is more focused on preventing Syrian Kurds from forming an autonomous region in northern Syria, along Turkey's border, that could embolden Turkey's own Kurdish minority.

On Wednesday, Turkish Prime Minister Binali Yildirim announced the operation had ended after its troops and allied rebels secured territory along the border between Turkey and Syria.

"Life is back to normal. Everything is under control," Yildirim said on Turkey's NTV news channel.

"Euphrates Shield has ended. If there is a need, a new operation will have a new name."