Canikli said he told Mattis that US support for such militants has enabled Kurdish rebels in Turkey "to grow and strengthen", posing an increasingly "existential" danger to Turkey.
Mattis spoke with his Turkish counterpart Nurettin Cenikli on the sidelines of a North Atlantic Treaty Organisation conference in Brussels on Wednesday.
"But throughout this, the one that has marked our communication is absolute honesty and transparency with one another. We continue to collaborate on ways to ensure their legitimate concerns are addressed".
Tillerson arrived in Turkey on Thursday for two days of what officials have said would likely be uncomfortable discussions between the allies, whose relations have frayed over a number of issues, particularly USA support for the Syrian Kurdish YPG militia, seen as terrorists by Turkey.
Turkey's president, Recep Tayyip Erdogan, is fuming over USA assistance to Kurdish fighters near his country's border.
YPG to fight against the PKK?
Top U.S. diplomat Rex Tillerson and Turkey's Tayyip Erdogan had a "productive and open" talk on Thursday about improving ties strained recently over their policies on Syria, in a meeting following weeks of escalating anti-American rhetoric from Ankara.
But Cavusoglu warned Washington that ties were at a "critical point" where relations would "be fixed or... completely damaged".
The specter of a U.S. "I told him that this is not a realistic approach".
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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.
Canikli made clear that Turkey's demand from its ally is to "end its cooperation with the YPG and to stand with Turkey against its existentialist terror threats".
The US has "never given heavy arms" to the YPG and, therefore, there is "nothing to take back", Tillerson said. Turkey's military campaign against Kurds in northern Syria has alarmed the USA leaders who have watched as the fighting has sapped energy from the fight against remaining IS strongholds.
Mattis, however, underlined the need for a renewed focus on the fight against ISIL as the group was seeking resurgence in Syria and Iraq in 2018.
Turkey is the main Muslim ally of the United States within North Atlantic Treaty Organisation and one of Washington's most powerful friends in the Middle East dating back to the Cold War era.
Erdogan has accused the United States of "building an army of terror" on his border and, in extraordinary language coming from a fellow North Atlantic Treaty Organisation ally, threatened to "drown" US-backed forces in Syria. "We declare from now; this kind of plot can not cast a shadow on Turkey's rightful struggle", he said on February 15.
Turkey has been attacking the Kurds in northern Syria for the past three weeks, despite American calls for restraint. If they are there, of course, we will not ask anybody's ID during the operation.
His statement came hours after Canikli said Mattis had told him the US was working on a plan to take back heavy weapons delivered to the YPG.