But the YPG is also a key component of a US-backed Kurdish-Arab alliance fighting the Islamic State group in Syria.
The Pentagon is seeking hundreds of millions of dollars to train Syrian fighters near the Turkish frontier while tamping down Ankara's fears of a Kurdish-led border force.
As the US, Russia and Syria's Assad regime watch Turkey's military operation against Kurds in northwest Syria grind on, Ankara is pointing fingers.
"The two sides are at a strategic impasse", Mr. Stein said in an interview Wednesday. They are the target of Turkey's operation "Olive Branch", which aims to create a Turkish-controlled buffer zone between Turkey and Syria.
Expect more pledges in the coming days while Rex Tillerson tours the Middle East, but it will likely be far short of what Baghdad says it needs. Turkey considers the YPG to be a terrorist organization, alleging it is an extension of a Kurdish group fighting for autonomy in Turkey for decades.
"The US is not touching ISIL (Islamic State of Iraq and the Levant) members in Syria as an excuse to continue working with the YPG/PKK (Kurdistan Workers' Party) terrorist groups", he added.
Meanwhile, Foreign Minister Mevlüt Çavuşoğlu again stressed that Turkey has "lost confidence" in the US, saying Ankara wants "action on the ground" rather than words. If President Tayyip Erdogan keeps his promise of pressing further east is set to pose a real threat of the collision of these two allies in North Atlantic Treaty Organisation.
Turkish officials have said Trump agreed to stop sending United States arms to the YPG in November, but USA weapons assistance to the group has continued, according to the Pentagon's inspector general.
Despite Washington's concerns, Mr. Erdogan himself has vowed to expand the operation even further into Syria toward the town of Manbij - and warning American troops stationed there not to get in the way. The United States sent high ranking army officers into Manbij, riding in vehicles prominently displaying USA flags, accompanied by a New York Times reporter to make sure the message was received in Ankara.
State Department spokeswoman Elizabeth Nauert told reporters in Washington on Tuesday that "as amusing as the comment was", she has a policy of not responding to every quip by every foreign leader. "So the U.S.is always going to advocate for an electoral process that respects the rights of its citizens to make the choices the citizens want to make and the full participation of citizens in those elections", he said.
While the United States means to work with Turkey to address its security concerns, the official said the U.S. goal is, "above all else, keeping everything focused on the defeat-ISIS fight, which is not over".
But Turkish officials do not appear to be mollified, at least in public.
"It is very clear that those who say "we will respond aggressively if you hit us" have never experienced an Ottoman slap", Erdogan said, in an apparent reference to comments made by US Lieutenant General Paul Funk during a visit to the northern Syrian city of Manbij last week.