Move comes a day after Turkey summoned Russian, Iranian ambassadors.
The U.S. weapons training of PKK/PYD terrorist organization members was discussed when Kosnett was summoned to the ministry, the source, who spoke on condition of anonymity due to restrictions on talking to the media, said.
The U.S. and the coalition have largely ignored PYD/PYG links to the PKK, which the U.S., EU, and Turkey lists as a terrorist group.
Anadolu Agency previously reported that the PKK/PYD terrorist organization, which has seized a quarter of Syrian territory, was forming a so-called army with the support U.S.
Also previously, the U.S. said they would continue to support the PKK/PYD in Syria's eastern Raqqah and Deir ez-Zor province, home to some of the country's most productive oilfields.
The latest news comes after the U.S. Central Command (CENTCOM) Commander Gen. Joseph Votel announced on Dec. 22, 2017 that they would establish border forces in Syria, which he said would help prevent resurgence of Daesh.
A group of around 400 terrorists were reportedly trained by the U.S. through the Pentagon and the CIA near eastern Aleppo's Tishrin Dam on the Euphrates River and in southern Hasakah province.