Turkey on Friday warned Washington that any meeting with the leader of the Kurdish-led Syrian Democratic Forces (SDF) risked "legitimizing terrorists".
US President Donald Trump on Thursday said he had talked with Mazlum Abdi, commander of the SDF which fought against extremists in Syria, and that he had "really enjoyed" the conversation.
In a tweet on Wednesday, Trump thanked Mazlum and said: "I look forward to seeing you soon", raising fears in Turkey of a possible face-to-face meeting between the two men in the United States.
"If you start legitimizing terrorists like this, tomorrow you will end up meeting with Baghdadi as well," Turkish Foreign Minister Mevlut Cavusoglu said in televised remarks.
Abu Bakr al-Baghdadi is the head of ISIS extremist group.
"It is not acceptable for our allies to meet with a terrorist wanted under a red notice," Cavusoglu told reporters in Baku.
"We have informed the US of all of this in a written note," the minister added.
Turkey says there is an Interpol red notice for Abdi, which Turkish NTV broadcaster reported had been issued in 2011.
A group of American senators including Lindsey Graham earlier this week urged the US State Department to expedite a visa for Abdi to enable a visit where he can speak to officials and lawmakers on the situation on the ground in Syria.
Turkish Justice Minister Abdulhamit Gul earlier on Friday said Turkey will demand that US authorities detain Mazloum as soon as he enters the United States.
He said the foreign ministry had conveyed the extradition request to Washington.
Gul told reporters in the Turkish border town of Akcakale that Turkish diplomats had contacted their US counterparts to remind them that Abdi was a wanted individual.
Relations between Turkey and the US are particularly tense after Ankara launched a cross-border offensive on October 9 against the Kurdish YPG, whose fighters make up the bulk of the SDF.
But there have also been strains over Washington's failure to extradite Fethullah Gulen, accused by Ankara of ordering the 2016 failed coup. which Gulen has denied.
