"We shared our concerns about the U.S. giving armed weapons' training to members" of the Syrian Kurdish Democratic Union Party's (PYD) militia with the U.S. charge d'affaires Philip Kosnett, Turkish foreign ministry sources said.
In Washington, a State Department spokesman confirmed the meeting occurred but said "beyond that we aren't going to read out any details of the conversation".
But in a major potential obstacle for Sochi, Turkey says it will oppose any talks involving the Syrian Kurdish militia the Peoples' Protection Units (YPG), which Ankara views as a terror group.
Earlier, Ankara's Foreign Minister Mevlut Cavusoglu stated that Syrian armed forces have been carrying out attacks on the so-called moderate opposition in the province of Idlib under the pretext of fighting terrorism.
Cavusoglu repeated Turkey's red line over its presence in Sochi by saying that: "We have said we will not be in any environment... where the YPG is present". Turkish Foreign Minister Mevlut Cavusoglu warned Moscow and Tehran that they must fulfill their duties under the de-escalation zone accord struck with Ankara a year ago.
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.
In October, the YPG and their allies announced the capture of ISIL's self-declared capital of Raqqa in Syria after a four-month operation.
Ambassadors of the two countries were called in to express Ankara's displeasure over the continuing attacks in Idlib.
Russia, Iran and Turkey are supposed to be the guarantors of last year's accord but Moscow and Tehran appear bent on reneging on their role to de-escalate fighting in the area, home to almost 2 million Syrians, to serve their own agenda.
It will be remembered that most of the opposition forces have been relocated to Idlib after being forced to withdraw from other parts of the country.
The three countries had agreed a year ago to establish a "de-escalation zone" in the opposition-held Idlib province and surrounding region, which borders Turkey.
Humanitarian aid organisations, rescuers and activists allege the Syrian and Russian air forces have struck hospitals, schools and marketplaces in congested residential areas in rebel-held towns.
Turkish foreign minister Mevlut Cavusoglu said in an interview broadcast on Turkish TV channels,"Iran and Russian Federation need to carry out their responsibilities".