In Afrin, the Kurdish People's Protection Units (YPG) could do little when Syrian Arab fighters backed by NATO's second-largest army thrust into the city on Sunday.
"Most of the terrorists escaped", - said Recep Tayyip Erdogan, the Turkish channel NTV. The European Union's top diplomat also criticized the Turkish military offensive in Afrin, calling on Ankara to work to halt the fighting in Syria.
Around 250,000 civilians have left in recent days after pro-Ankara fighters took the surrounding region and all but encircled the city, fleeing southwards to territory still held by the YPG or controlled by the Syrian regime.
"I am anxious about this", she told reporters on Turkey's "Operation Olive Branch", saying worldwide efforts in Syria should be "aimed at de-escalating military activities and not escalating them".
The Kurdish-dominated force has seized huge areas of northern and eastern Syria following their offensive against the Islamic State group, with U.S. backing.
"By controlling Afrin city centre yesterday, we have passed the most important step of the Olive Branch operation", Erdogan told a gathering of judges and prosecutors in Ankara.
He said since the start of Turkey's Operation Olive Branch, 3,622 Kurdish YPG and ISIS militants have been "neutralised" (killed, injured or captured).
Turkey on Monday rejected claims that the terrorist YPG/PKK had "withdrawn" from the town of Afrin, northwestern Syria before Turkish-backed forces liberated the city center on Sunday.
Spokeswoman Heather Nauert said in a statement Monday that the offensive forced the majority of the predominantly Kurdish population of Afrin to evacuate from the town. "We did that before, we did that in Afrin today and we will do it in Manbij and the east of the Euphrates in Syria tomorrow", Cevik wrote. Turkey's threat to attack Manbij, where USA troops are based, has put Ankara at loggerheads with Washington, and talks between the North Atlantic Treaty Organisation allies has so far yielded no agreement.
"This will be a very complex and complicated situation for those who remain in Afrin and it will be hard for those who are displaced and who at the present moment are not yet in a very stable situation where we can deliver humanitarian assistance", he said. Those areas are controlled by US -backed Syrian Kurdish forces, and USA troops are stationed there. "If you are unable to handle it, we can suddenly come into Sinjar one night and clean the PKK from there".
He said the PYD/PKK terrorists had also carried out rockets attacks from "Euphrates Shield" operation areas on Kilis.
Already, thousands of Kurdish fighters have been redeployed away from front lines with IS to take part in the Afrin battle, threatening to distract from the fight against the extremists.
The U.S. State Department said it was "deeply concerned" over the humanitarian situation following Turkey's capture of Afrin.
The success of Turkish led forces in Afrin is threatening to create its own momentum for a further escalation in the military conflict.