A young Syrian boy has died after a boat capsized off the Greek island of Lesbo - the first official fatality since Turkey opened its border last week to let migrants reach Europe.
The European Union's chief executive Ursula von der Leyen said today it was impermissible for Turkey to let refugees and migrants cross into Europe.
Separately, two Turkish security sources told Reuters a Syrian migrant had died from injuries at the weekend after Greek security forces intervened to prevent migrants crossing from Turkey into Greece, but Athens branded the claim "fake news".
More than 10,000 migrants, mostly from Syria, other Middle Eastern states and Afghanistan, have reached Turkey's land borders with EU states Greece and Bulgaria since Ankara said last Friday it would stop keeping them on its territory.
Further south, at least 1000 migrants have reached Greece's eastern Aegean islands since Sunday, Greek police said.
"This is an invasion," Development Minister Adonis Georgiadis told Skai TV.
The surge, which has seen Greek and Turkish police firing tear gas into crowds of families caught in the no-man's land between the two borders, has revived memories of the 2015-16 refugee crisis, when more than a million people arrived in Europe from Turkey.
"We have children four days without food," one man shouted from behind a wall of barbed wire near the Kastanies border post as Greek riot police stood ready to repel any breaches of the frontier. Nearby soldiers unrolled more coils of barbed wire.
The migrants, some with white flags, then chanted "peace" in English.
Greek Prime Minister Kyriakos Mitsotakis's office said he had discussed the border situation with US President Donald Trump who it said had "recognised the right of Greece to enforce the law on its borders". Trump has built a wall to deter migrants trying to enter the United States from Mexico.
The boat which capsized off Lesbos had been escorted there by a Turkish vessel, the Greek coastguard said, underlining the escalating tensions between Ankara and Athens. The dead boy was aged about six, they said, but provided no other details.
Another dinghy with about 30 Afghans arrived on Lesbos early on Monday, a Reuters journalist reported from the island.
About 4000 people are believed to have drowned in the Aegean during the 2015-16 crisis trying to reach Greece, while some 42,000 migrants are still living in severely overcrowded camps on the Greek islands.
2016 EU accord
The latest migrant surge follows Turkey's decision to stop enforcing a 2016 accord with the European Union whereby it stopped migrants entering the bloc in return for cash.
Turkey, already home to 3.7 million Syrian refugees, has another million arriving on its doorstep from a new surge of fighting in northern Syria and says it cannot handle any more.
Greek officials have accused Turkey of orchestrating a coordinated effort to drive migrants across the frontier.
One Greek policeman accused Turkish soldiers at the Kastanies border gate of "giving cutters" to migrants to cut holes in the fence to get through. Reuters could not independently verify the report.
Some migrants camped near the border had erected makeshift tents or built bonfires to stay warm.
"We're going to keep waiting here because we left our homes. Those of us who had homes, who had things, we sold them and got money for them. If we want to go back we will sleep in the streets," said Jamal Kassar, a Syrian migrant.
"What can we do, we're stuck here, we can't go back home and we can't cross (the border)."
A Greek government spokesman said a video circulating on social media showing a young man with wounds to the head laid out on the ground near the border was "fake news". Two Turkish security sources said the Syrian man had died of his wounds.
Greeks living near the border said they were tired of seeing waves of migrants passing through.
"People are exasperated, they yell, they curse, they are tired of seeing this sight here, immigrants passing," said Poppy Katrivesi, who runs a tavern in Kastanies.
The EU's chief executive, Ursula von der Leyen, expressed sympathy with Turkey over the conflict in Syria but said its decision to let refugees and migrants cross into Europe "cannot be an answer or solution".
German Chancellor Angela Merkel, whose decision to open Germany's borders to refugees helped swell the 2015 influx, also said Turkey should not express its dissatisfaction with the EU "on the back of refugees".
Von der Leyen was due to visit the Greek-Turkish border tomorrow with Mitsotakis.
Prime Minister Boyko Borissov of Bulgaria, which also shares a land border with Turkey, was due to hold talks in Ankara today with Turkish President Tayyip Erdogan on the crisis.
Erdogan opened Turkey's border after at least 33 Turkish soldiers sent to Syria to monitor a crumbling ceasefire there were killed last week.
EU interior ministers will hold an extraordinary meeting on Thursday to discuss the situation at the bloc's border with Turkey, and specifically how they can support Greece and Bulgaria patrol their frontiers.