Greece has blocked any new asylum applications for the next month after Turkey "opened the doors" for migrants to travel to the EU.
Greek officials earlier said they had stopped nearly 10,000 migrants crossing the land border with Turkey.
Prime Minister Kyriakos Mitsotakis said Greece had increased "the level of deterrence at our borders to the maximum."
Turkey says it cannot deal with the amount of people fleeing Syria's war.
Turkish President Recep Tayyip Erdogan said he was allowing migrants to try to get into neighbouring EU member states Greece and Bulgaria as of Friday.
His decision came after at least 33 Turkish soldiers were killed in air strikes in Idlib province in northern Syria this week.
Turkey is hosting 3.7 million Syrian refugees, as well as migrants from other countries such as Afghanistan - but had previously stopped them from leaving for Europe under an aid-linked deal with the EU.
But Mr Erdogan accused the EU of breaking promises made in 2016, when Ankara agreed to help shore up the EU's south-western border.
The EU's border protection agency Frontex said it was on "high alert" on Europe's borders with Turkey.
What's happening in Greece?
Prime Minister Mitsotakis announced the suspension in asylum applications on Twitter on Sunday evening, and said Greece had invoked an emergency clause of an EU treaty "to ensure full European support".
"The borders of Greece are the external borders of Europe. We will protect them," he wrote, adding that he would be visiting the Evros land border with Turkey with European Council President Charles Michel on Tuesday.
"Once more, do not attempt to enter Greece illegally - you will be turned back," he warned.
The Greek government said almost 10,000 migrants were blocked from entering Greece in 24 hours.
Some migrants tossed stones, metal bars and tear gas canisters when stopped at the border. Greek border guards fired tear gas.
Separately, Greek police say at least 500 people on seven boats have reached the Greek islands of Lesbos, Samos and Chios, where camps for migrants are already severely overcrowded.
Seven boats carried more than 300 people to Lesbos, four arrived on Samos with 150 and two on Chios with a combined total of 70 to 80 people, an official told the Reuters news agency.
Groups of migrants have also been seen wading through a river to Greek soil at Kastanies.
Many blocked migrants have been sent to Evros, an area along the Turkey border.
Greek deputy defence minister Alkiviadis Stefanis accused Turkey of encouraging migrants to make the trip.
"Not only are they not stopping them, but they are helping them," he told Greece's Skai TV.
There were clashes between migrants and Greek police on Saturday after President Erdogan effectively gave the all-clear for migrants to head for the EU.
The EU said it was assisting Greece and Bulgaria - which also borders Turkey - in protecting the bloc's parameters.