A delegation from the Syrian Democratic Council (SDC) -- the political wing of the Syrian Democratic Forces (SDF) -- travelled to Brussels to urge the EU to take concrete measures to punish Turkey.

The EU has urged Turkey to halt the assault but has not taken any action, though the bloc's foreign ministers will discuss the crisis at a regular meeting on Monday.

"We want an urgent intervention on this crisis, and these attacks should be stopped quickly. Air space should be closed for Turkish flights so that air attacks can be stopped," senior SDC figure Ilham Ahmed told reporters in Brussels.

"All European states should freeze their relations by withdrawing their ambassadors from Turkey immediately."

The SDF, then allied to the United States, played a key role in the fight to eliminate the Islamic State group's "caliphate", but Ankara regards the Kurdish fighters as terrorists linked to insurgents inside Turkey.

Turkish President Recep Tayyip Erdogan on Thursday warned Brussels against further criticism of the operation, threatening to "open the doors" and send some 3.6 million refugees from the Syrian war that it hosts to Europe.

Ahmed lamented the withdrawal of US troops from the border region earlier this week, which effectively cleared the way for Turkey to move in.

"If American forces were there, Turkey would not attack us, but unfortunately with the American withdrawal they put us in danger," she said, urging Washington to remember the sacrifice made by Kurdish forces in the fight against IS.

"We want them to consider that we have paid a big price -- 11,000 martyrs -- and to stay beside us."