European Union member states have said the bloc "strongly rejects" what it sees as Turkey's use of migrants for political goals.
In a statement agreed by ministers at a meeting in Brussels, the 27 states said the "situation at the EU's external borders is not acceptable."
Earlier, Turkish President Recep Tayyip Erdogan's government denied that it was using the threat of a wave of migrants to "blackmail" the EU.
But the EU statement said the meeting "strongly rejects Turkey's use of migratory pressure for political purposes".
Ankara wants Brussels to step up support for refugees from Syria and Turkey's increasingly intense confrontation with the Damascus regime.
But EU members insist Turkey must stick to a 2016 deal in which it agreed to prevent refugees and migrants from crossing to Greece in return for billions of euro in aid.
"Illegal crossings will not be tolerated," the statement said.
"In this regard, the EU and its member states will take all necessary measures, in accordance with EU and international law.
"Migrants should not be encouraged to endanger their lives by attempting illegal crossings by land or sea."
The ministers urged Turkey to "relay this message and counter the dissemination of false information."
Yesterday, EU leaders pledged €700m to help Greece handle the crisis.
Today's meeting in Brussels took place after Greek security forces used tear gas and water cannon on hundreds of migrants trying to cross the border from Turkey.
More than 10,000 migrants have been trying to breach the frontier since Turkey said last Thursday that it would no longer abide by the 2016 agreement.
Turkish officials said Greek forces had killed a migrant on the border today, a claim denied by Greece.
Plumes of black smoke drifted above the Kastanies border crossing as Greek soldiers fired warning shots in the air.
A witness saw teargas canisters being thrown from the Turkish side of the border towards Greek police over a high razor wire fence.
The Greek government later released a video it said showed Turkish border guards were firing the canisters.
Turkish officials said Greek forces had killed a migrant and wounded five others today at the border, prompting Greek government spokesman Stelios Petsas to say: "Turkey is disseminating fake news ... I dismiss this categorically."
Greece similarly denied a Turkish claim yesterday that its forces had killed three migrants at the border.
Video footage today showed migrants carrying an injured comrade away from the border. It is unclear how he had been hurt.
Turkey, which already hosts 3.6 million Syrian refugees and faces another influx from an upsurge in fighting in northwest Syria, says the EU is not providing enough help to deal with the scale of the migrant crisis.
Erdogan demands EU help in Syria to end migrant crisis
Turkish President Recep Tayyip Erdogan told members of his ruling AK Party in Ankara that Greece, and the EU generally, must "act in line with the Human Rights Declaration and respect the migrants arriving on their land".
The EU fears a repeat of the 2015-16 migrant crisis, when more than one million migrants came to western Europe via Turkey and the Balkans, straining European security and welfare services and boosting support for far-right parties.
Hungarian Prime Minister Viktor Orban, known for his tough anti-immigrant stance, said 130,000 migrants had already passed the Greek border from Turkey and that they must be stopped as far south as possible. It is unclear how he arrived at that figure, which is much higher than any previously mentioned.
Prime Minister Boyko Borissov of Bulgaria, which also shares a land border with Turkey, called after talks with EU officials today for renewed dialogue with Ankara on how to handle the migrants and shore up regional stability.
An unknown number of migrants have also arrived on Lesbos and other Greek islands from the nearby Turkish coast in the past week, though choppy seas discouraged sailings for a second consecutive day.
A navy ship docked at Lesbos port will take in 508 migrants who have arrived since 2 March once they have been identified, a Greek coastguard official said. He did not say where the ship would take them.
Hussein, in a group of about 100 migrants which arrived in Lesbos four days ago and has been camping on the shore, said he left Afghanistan with his 17-year-old brother a month ago and crossed Iran and Turkey before reaching the island by dinghy.
"Our future is going to be bright because I am an educated person so I don't need much help. I want to complete my education and then I will need a job," he said.