"We shared our concerns about the US giving armed weapons' training to members" of the Syrian Kurdish Democratic Union Party's (PYD) militia with the US charge d'affaires Philip Kosnett, Turkish foreign ministry sources said.
The sources did not give any further detail.
Kosnett is currently the most senior American diplomat in Ankara after the departure late last year of the ambassador, John Bass. His replacement has yet to be named.
While the US views the Peoples' Protection Units (YPG) militia as the most effective fighting force on the ground against Islamic State (IS) extremists, Ankara calls it a "terrorist" organisation linked to outlawed Kurdish militants in Turkey.
Turkey claims both the YPG and the PYD are a branch of the Kurdistan Workers' Party (PKK), which is proscribed as a "terror" organisation by Ankara, Washington and Brussels.
Relations between Washington and Ankara have been tense over multiple issues including a US decision last year to deliver weapons to the YPG.
But in November, Turkish officials said US President Donald Trump told them in a phone call that Washington would no longer supply arms to the YPG.
There is also tension over a US failure to extradite the Pennsylvania-based Muslim preacher Fethullah Gulen whom Turkey says ordered the failed coup of July 2016, as well as the US conviction earlier this month of a Turkish banker over a scheme to help Iran avoid US actions.
Gulen denies the charges.