Greece accused Turkey of helping dinghies filled with migrants sailing to Europe to reach Greek waters.
On Friday, Athens said Turkish ships helped migrant vessels enter Greek waters overnight on six occasions.
The countries are in dispute over several issues, including energy resources in the Mediterranean, and tension was heightened last year when thousands of asylum seekers in Turkey tried to storm the Greek land border.
“The Hellenic coastguard reported multiple incidents of the Turkish coastguard and Navy accompanying flimsy migrant boats to the border of Europe in an effort to provoke an escalation with Greece,” said Notis Mitarachi, the Greek Minister of Migration and Asylum.
“It is beyond doubt that these migrants left from Turkish shores and, given the fact they were supported by Turkey, were not at risk.
“We call on Turkey to stand down and stop this unwarranted provocation, return these migrants safely to Turkey and live up to the 2016 EU-Turkey joint statement of migration.”
Greece said that in another incident, the crew of a Turkish coastguard vessel harassed those onboard a Greek coastguard ship.
The incidents took place in the narrow stretch of water between the Greek island of Lesbos and the Turkish coast.
The area is a major route for migrants trying to reach the EU from North Africa.
The Turkish coastguard, plus numerous refugee rights organisations and aid groups, have accused the Greek coastguard of conducting pushbacks.
This is the illegal summary deportation of migrants, without allowing them to apply for asylum, even after they have reached Greek territory.
Greece countered that Turkey is not only failing to crack down on migrant smugglers operating from its shores, but encourages and escorts migrants trying to enter Greece illegally.
