The YPG are now leading the Syrian Democratic Forces (SDF), which is composed of mainly Kurdish and Arab militias.
Asked about the unusual nature of the meeting, a State Department official said that Tillerson has "met before with President Erdogan, and he's okay with the Foreign Minister (Cavusoglu) doing the translation". We're going to lock arms.
Tillerson delivered a stark warning to Turkey on that score, saying he wanted to "at least ensure they understand what might be at risk in that particular transaction".
The Turkish offensive against the YPG in Syria has so far been limited to Afrin, a border region where the United States is not believed to have troops on the ground.
In a proposal that could signal an important breakthrough in efforts to overcome the allies' stark differences over Syria, a Turkish official told Reuters that Turkey had proposed that Turkish and United States forces could deploy jointly in Manbij.
Turkey has threatened to attack US-allied Kurdish forces in Manbij, whom they regard as terrorists.
Neither Tillerson nor Cavusoglu, the Turkish foreign minister, responded directly to a question about the Reuters report of a possible joint deployment to Manbij.
Tillerson was in Ankara to discuss growing tensions over the U.S. military's anti-Islamic State (IS) alliance with the YPG, a Kurdish militia in Syria.
Speaking at a joint news conference with US Secretary of State Rex Tillerson, Cavusoglu also said Tillerson's visit marked a critical point for the future of the relations between two North Atlantic Treaty Organisation allies. We spoke to not only Russian Federation but with other countries too.
Manbij is strategically important to the US-led coalition's goal to contain and defeat ISIS, Tillerson said.
The Turkish minister also reported Mattis as saying the USA was developing plans to take back weapons supplied to the Syrian Kurds.
Even as Tillerson called out Turkey's increasingly dire record on democratic norms, and its plans to purchase Russian military equipment in violation of United States sanctions, he stressed the need to move forward.
The US and Turkey will create working groups to tackle unresolved areas of tension, including Washington's anti-ISIS partnership with a Kurdish group Turkey staunchly opposes. Tillerson said a priority will be given to the issue of Manbij as the two sides work together.
"But it's not just Manbij".
Both Tillerson and Cavusoglu that the countries have found themselves at "a crisis point", and have agreed to address "critical issues" in the bilateral relations.
He said he recognised Turkey's legitimate right to defend its borders, but called on Ankara to show restraint in the Afrin operation and avoid actions that would escalate tensions in the area.
Tillerson's visit came as anti-U.S. rhetoric from Turkish officials, including Erdogan and Cavusoglu, had spiked in recent days, with the president earlier this week suggesting that the Americans might be deserving of an "Ottoman slap", a reference to the Ottoman Empire's one-time might.