Erdogan has vowed to crush it in the wake of Trump's decision to pull troops out.
On Monday Turkish President Recep Tayyip Erdogan held a phone call with his United States counterpart Donald Trump, discussing the idea of establishing a 32-kilometer (20-mile) terror-free safe zone in northern Syria.
A spokesperson for Kurdish umbrella organization Movement for a Democratic Society (TEV-DEM) said on Tuesday that Kurdish militia would not accept a Turkish-controlled security zone in northern Syria, according to Kurdish news agency ANHA.
Erdogan conditioned setting up the safe zone on clearing the area of the USA -backed Kurdish People's Protection Units (YPG/YPJ), who Ankara believes are affiliated with the Kurdistan Worker's Party (PKK) communist terrorist group, Hurriyet Daily News reports.
The Turkish president explained that safe zone negotiations between the United States and Turkey were still needed to define what logistics the US and its coalition partners will provide for securing the territory and reconstructing the area after the return of Syrian refugees.
Trump confirmed this in a tweet later, but referred to the proposed area as a "safe zone".
However, on Monday after the phone call, Trump expressed the desire to work together to address Turkey's security concerns in northeast Syria.
National Basketball Association looking into circumstances of McCaw signing
The person spoke on condition of anonymity because no details of the probe have been revealed publicly. The NBA will look into the Cavaliers signing and release of Patrick McCaw .
Hardik Pandya-KL Rahul controversy: BCCI CEO speaks to suspended stars
Meanwhile, the pair has tendered an unconditional apology to the cricket board for their comments on the talk show. Sreesanth said that he would just walk away from the game if he realised that he is not up to scratch.
Saudi refugee granted asylum, flying to Canada
A Saudi teenager who fled her homeland for Thailand to escape her "abusive" family is to fly to Canada, Thai officials say. Alqunun had previously said on Twitter that she wishes to seek refuge in Australia.
For months, the Turkish military has been preparing to launch an operation against fighters from the YPG, the armed wing of the Kurdish Democratic Union Party (PYD) that has maintained control over most of northern Syria with the help of US troops fighting the Islamic State (ISIS/ISIL) in the area. We have said it in the past.
On Saturday, more than 600 people were evacuated from the remaining IS holdout in eastern Syria, a monitor said, as US-backed fighters prepare for a final assault on the area.
Lavrov's comments come as Turkey sets out plans to create a "safe zone" along its border with northern Syria.
Ankara regards the YPG as an offshoot of the Kurdistan Workers' Party (PKK), which has waged a deadly war for autonomy in southeastern Turkey since 1984, and describes the armed group as "terrorists".
Speaking to reporters in parliament, Erdogan also said he would most likely meet Russian President Vladimir Putin on January 23.
Turkey has threatened to attack the YPG in the Syrian city of Manbij. Despite the posturing of Trump and Erdogan, Pompeo and his Turkish counterpart, Foreign Minister Mevlut Cavusoglu, are said to be in accord on the "importance of continuing U.S".
In Sunday's tweet, Trump also warned the Kurdish forces not to "provoke Turkey".