The United States sought to play down a diplomatic rift with Turkey on May 27 after U.S. commandos were caught on camera wearing badges of a Syrian Kurdish group.
Ankara reacted with fury after AFP published pictures of U.S. special forces working with the Kurdish PYG forces in northern Turkey and wearing their insignia.
Washington regards the PYG militia as a valuable ally in the fight against the Islamic State of Iraq and the Levant (ISIL) in Syria, but Turkey sees the group as terrorists.
Turkish Foreign Minister Mevlüt Çavuşoğlu declared the U.S. alliance with the group "unacceptable" but the State Department denied that relations are in crisis.
"We understand Turkey's concerns, let me make that clear, and we continue to discuss this as well as other concerns Turkey has," spokesman Mark Toner said.
Toner said that Washington does not regard the YPG, which operates in Syria, as part of the outlawed Kurdistan Workers’ Party (PKK).
"With respect to Turkey's comments about these photos we've been very clear... about our belief that the YPG is not connected to the PKK," Toner said.
"On the contrary, we believe the YPG as well as other forces in northern Syria are effectively taking the fight to ISIL," he added.
"And we're going to continue to support them with our assist and support operation."
Toner thanked Turkey for supporting the coalition against ISIL, which U.S. officials variously refer to as ISIL, ISIS or Daesh.
"Turkey's been an active member of the anti-Daesh coalition, continues to be an active member. We're grateful for Turkey's support," he said.
"The goal here is to destroy and degrade Daesh and to remove them from the battlefield," he said. "Now, are there disagreements between members of the coalition as to how we proceed and with who we're cooperating on the ground?" he said.
"I'm not going to say that there aren't, and obviously Turkey's made very clear its feelings about the YPG."