EU Council President Donald Tusk on Friday condemned as attempted "blackmail" a threat by the Turkish president to allow millions of refugees to head to Europe if the bloc criticises Ankara's offensive in Syria.

"Turkey must understand that our main concern is that their actions may lead to another humanitarian catastrophe, which would be unacceptable," Tusk said on a visit to EU member Cyprus. 

"Nor will we ever accept that refugees are weaponised and used to blackmail us. That is why I consider yesterday's threats made by President (Recep Tayyip) Erdogan totally out of place," he added.

Erdogan made his comments on Thursday in the face of mounting condemnation from European governments of Ankara's long-threatened operation to enforce a buffer zone in northeastern Syria to accommodate some of the 3.6 million refugees currently living in Turkey.

"Hey EU, wake up. I say it again: if you try to frame our operation there as an invasion, our task is simple: we will open the doors and send 3.6 million migrants to you," the Turkish leader said.

Under a 2016 agreement with the EU, Turkey agreed to prevent refugees from leaving towards Europe in exchange for six billion euros and visa-free travel for its citizens, but has frequently criticised the lack of assistance from Brussels.

Tusk condemned Turkey's offensive, launched Wednesday, saying it was "of grave concern and should stop". 

"A military intervention will only make matters worse," he added, saying it would exacerbate instability in the region, cause further civilian suffering and displacement as well as undermine the fight against the Islamic State group.