Turkey says the United States has yet to honour several pledges: to stop arming the YPG, to take back arms after Islamic State was defeated in Syria, and to pull YPG forces back from Manbij, a Syrian town about 100 km (60 miles) east of Afrin.
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.
A war of words between the North Atlantic Treaty Organisation allies has escalated ever since Turkey launched a military offensive into the Afrin region of northern Syria last month in an effort to root out Kurdish YPG fighters, who figure among a US-backed coalition of armed groups.
Secretary of State Rex Tillerson met for more than three and a half hours of tough discussions with Turkish leaders in an attempt to ease increasing tensions with a key North Atlantic Treaty Organisation ally - but without a translator or policy aides.
Canikli and Mattis arrived in Brussels to attend NATO Ministers of Defense meetings.
Mattis spoke with his Turkish counterpart Nurettin Cenikli on the sidelines of a North Atlantic Treaty Organisation conference in Brussels on Wednesday.
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.
"We also told him that YPG elements should be removed from the Syrian Democratic Forces [SDF]", he said.
But the rising US-Turkey tensions add to concerns about the unusual nature of Tillerson's meeting.
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. Turkey acknowledges the YPG as the outlawed Kurdistan Workers' Party's (PKK) extension in Syria and has been fighting against the group in the Afrin district of Syria since January 20.
The objective of this scenario would be isolating and putting Turkey into a hard situation by resurrecting ISIL in northern Syria, Bozdağ said.
But Syria is not the only cause of strained ties between Washington and Ankara.
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.
Tillerson, however, later said that Washington had "never given heavy arms" to the YPG, and there was therefore "nothing to take back". After McMaster's meeting with his Turkish counterpart, Cavusoglu warned that Turkey-US ties had hit a critical point and would either be repaired or be completely damaged.