NORTHERN SYRIA — The head of Kurdish forces in Syria said Tuesday that President Donald Trump promised to end Turkey's assault on their territory despite having made the decision to pull out of the region and abandon the U.S. allies in the fight against the Islamic State militant group.

Gen. Mazloum Kobani, commander in chief of the Syrian Democratic Forces, told NBC News in an interview that he recently spoke to Trump and was assured that "there would not be a massacre against the Kurds" and that Trump would stop the invasion immediately. But Turkish forces have pushed ahead with their attack on northeastern Syria, taking control of a strategic border town Thursday.

"I call on President Trump to fulfill his promise," Kobani said. "I want him to stay committed to his words."

The White House confirmed that a conversation between Trump and Kobani took place but made no comment on the content of the call. A senior administration official said the president spoke to both "Gen. Mazloum and President Erdogan" on Monday.

Vice President Mike Pence and Secretary of State Mike Pompeo met with Turkish President Recep Tayyip Erdogan in Ankara on Thursday in an effort to persuade him to implement a cease-fire. It also emerged that Trump wrote an extraordinary letter to Erdogan warning him not to be “a tough guy” and threatening tougher sanctions.

But Erdogan has vowed to never declare a cease-fire, telling reporters ahead of Pence's and Pompeo's arrival that he isn't worried about any sanctions from the United States.

Turkish forces launched their invasion last week to establish a "safe zone" for Syrian refugees and rid the region of Syrian Kurdish fighters, who it says are an extension of the separatist Kurdistan Workers' Party (PKK).

While the PKK is considered a terrorist group by the U.S., the Kurdish-led SDF has been crucial American allies in the war against ISIS.

Turkey-backed Syrian fighters gather on the road between the Syrian towns of Tal Abyad and Kobani on the Turkish border on Wednesday as Turkey and its allies continue their assault on Kurdish-held border towns in northeastern Syria. Bakr Alkasem / AFP - Getty Images

"But we see now that the Turkish assault has weakened that war [against ISIS] in a big way," Kobani said. "The Kurdish people will be destroyed, and there will be very large problems."

It's estimated that the SDF has held more than 10,000 ISIS members in detention centers and prison camps, but some of those detainees have escaped amid Turkish strikes.

Kobani warned "there is a big danger" of ISIS resurging if more members are freed and regroup.

"The fight against terrorism will fail," he said.

The U.S. could avoid these ramifications and repair feelings of mistrust and betrayal among the Kurds by reversing the error of pulling out troops which allowed Turkey to invade, he said.

Yet despite tough words to Erdogan, Trump also told reporters in the Oval Office on Thursday that the fight over the territory "has nothing to do with us."