Turkey accuses the YPG of being an offshoot of the Kurdistan Workers Party (PKK), which has been engaged in an armed insurgency against the Turkish state since 1978.
Both Turkey and the U.S. were in agreement that so-called "safe zones" should be created in northern Syria to prevent the YPG from encroaching on Turkish borders, but disagreed over the size of those zones.
Turkey has been pressing to control - in coordination with the USA - a 19-25 mile (30-40 kilometer) deep zone within Syria, running east of the Euphrates River all the way to the border with Iraq.
They gave no details but said Turkey's security concerns regarding the region would be addressed.
The US and Turkey have agreed to establish a new "safe zone" in north-eastern Syria, the US embassy in Turkey said in a statement on Wednesday, averting a new diplomatic crisis.
That put the United States in a hard position as a North Atlantic Treaty Organisation ally of Turkey but also a supporter of the YPG as its main frontline partner against the so-called Islamic State group.
Underlining that the meetings were positive and constructive, Akar said: "We gladly observed that our interlocutors approached our views on the Syria safe zone".
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Raab said "there's obviously going to be a lot of work to make that happen", but added that Trump had been "effusive in his warmth" for Britain.
The force controls large swaths of territory along the Syrian-Turkish border and is dominated by Syrian Kurdish fighters, whom Turkey considers a threat to its own security.
Turkey has said it must have ultimate authority over the safe zone, another point of divergence with the United States.
"If we don't do what is necessary today, we will have to do so by paying a high price later", Erdogan said, signaling a new operation into Syria after the 2016 Euphrates Shield incursion and last year's Olive Branch operation to drive Kurdish YPG fighters from the northern Syrian region of Afrin.
U.S. Defence Secretary Mark Esper said this week any Turkish operation into northern Syria would be "unacceptable".
"We witnessed with satisfaction that our partners grew closer to our position".
Turkey has in the past year reported that its soldiers have come under fire from the YPG in northern Syria. "But we said we wanted to act together with our friend and ally, the United States", state-owned Anadolu Agency quoted him as saying.
Turkish media outlets have often shown images in recent weeks of military convoys heading for the border area, carrying equipment and fighting units.