Earlier this week, Turkey demanded the USA expel the YPG from the Syrian Democratic Forces (SDF) coalition, which has been fighting Islamic State of Iraq and the Levant (ISIL) in Syria with support from the US.
"We demanded this relationship be ended, I mean we want them to end all the support given to the Syrian arm of PKK, the YPG", Turkish Defence Minister Nurettin Canikli told reporters in a briefing in Brussels, a day after meeting U.S. Defense Secretary Jim Mattis on the sidelines of a North Atlantic Treaty Organisation meeting.
Tillerson is in Ankara to discuss growing tensions over the U.S. military's anti-ISIS alliance with the YPG, a Kurdish militia in Syria.
With Turkey increasing its critical tone against the USA and implying that it won't hesitate to hit YPG positions in the Manbij city of Syria where American troops are stationed, talks between the two capitals have intensified to ease the bilateral and regional tension.
In Brussels, U.S. Defense Secretary Jim Mattis said the United States and Turkey are in open dialogue about their differences.
"I believe we are finding common ground and there are areas of uncommon ground, where sometimes war just gives you bad alternatives to choose from", Mattis told reporters on the sidelines of a North Atlantic Treaty Organisation meeting after his meeting with Canikli.
While Tillerson has taken a conciliatory tone saying this week the USA was "keenly aware of the legitimate security concerns of Turkey", officials in Ankara have been more blunt.
There is still no U.S. ambassador to Turkey after the departure of John Bass a year ago, and it was only in December that the two sides ended a row following tit-for-tat suspensions of visa services.
"We promise we will never cease fighting corruption", he said.
Ankara views the YPG as the Syrian branch of the militant Kurdistan Workers' Party (PKK) that has been fighting for an autonomous region inside Turkey since 1984.
Turkey has been attacking the Kurds in northern Syria for the past three weeks, despite American calls for restraint.
But Cavusoglu warned Washington that ties were at a "critical point" where relations would "be fixed or... completely damaged".
The two defense leaders are attending the year's first conference of North Atlantic Treaty Organisation defense ministers.
"We have reiterated our expectation that the USA should work together with its ally, Turkey, against terror organizations and not with terror organizations", he added.
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