A Turkish official accused Greek authorities on Monday of killing a migrant who was trying to breach their shared border, a claim Athens dismissed as "fake news".

"The fact that Greece uses tear gas and stun grenades, and that it has killed a migrant today is an inhuman approach," said Omer Celik, spokesman for Turkey's ruling Justice and Development Party (AKP), in a televised briefing.

A video published by the Turkish media, which has not been verified by AFP, shows a man presented as a Syrian, immobile on the ground with blood on his neck and face.

Greek officials rejected the authenticity of the images. "Video showing fatality on Greek-Turkish border is fake news," tweeted government spokesman Stelios Petsas.

Several thousand migrants have massed at the border after Turkey "opened the doors" for them to leave for Europe. German Chancellor Angela Merkel and EU migration commissioner Margaritis Schinas denounced the move Monday in comments to journalists in Berlin.

Turkey has around four million refugees, most of them Syrians -- but agreed in 2016 to prevent them leaving for Europe in exchange for billions of euros in assistance. Erdogan vowed Monday to keep the doors open for migrants heading for Europe, saying the European Union had not delivered the promised aid.

Greek authorities have used teargas and water cannons to push them back, leading to clashes.  Another unverified video released by the Turkish authorities appears to show Greek coastguards harassing and firing rounds near a boat full of migrants.