Convoys of people appeared heading towards the land and sea borders of Greece, which was a gateway for hundreds of thousands of asylum seekers into Europe in 2015 and 2016.
"They (the migrants) didn't come here on their own. They are being sent away and being used by (our) neighbour, Turkey," Greek Public Order Minister Michalis Chrysohoidis told reporters near the northern Greek border town of Kastanies.
"Greece... faced an organised, mass and illegal attempt to violate its borders and it withstood this attempt," government spokesman Stelios Petsas said, adding that by Saturday morning authorities had prevented more than 4000 people from entering Greece.
The crisis is the first big policy test for Greek Prime Minister Kyriakos Mitsotakis, who was elected in July and promised a tougher stance on immigration.
Turkey hit back at the Greek accusations.
"Look who's lecturing us on international law! They're shamelessly throwing tear gas bombs on thousands of innocents piled at their gates," Turkish Foreign Minister Mevlut Cavusoglu tweeted, along with pictures of hundreds of people sitting outside the Greek border post.
"We don't have an obligation to stop people leaving our country but Greece has the duty to treat them as human beings!"
The European Union said it was supporting Greece - and its neighbour Bulgaria, which also shares a border with Turkey - in protecting the bloc's borders, but also sought to placate Ankara.