Greek troops and riot police are on high alert along the land border between Greece and Turkey, the main flashpoint in an escalating row between the European Union and Ankara over how to deal with a new wave of refugees and migrants.

Some 10,000 refugees and migrants have been trying to breach the border since Turkey said last Thursday it would no longer uphold a 2016 accord with the EU to keep refugees and migrants on its territory in return for billions of euros in aid.

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Greek authorities said the border had been quiet overnight, in contrast with the clashes seen from Friday to Monday, when police used tear gas against the people, including women and children, stuck in the no-man's land.

"There were only a few attempts today. Let's hope they get the message," a machine gun-toting army officer told Reuters news agency near the Kastanies border crossing.

Army jeeps patrolled the area and roads leading to the Evros river, which marks the Greek-Turkish border, remained shut.

"Greece's borders are also Europe's borders," Greek Prime Minister Kyriakos Mitsotakis said in a statement released before a planned inspection tour of the area later on Tuesday with the heads of the three main EU institutions.

The presidents of the executive European Commission, the European Council - which represents national governments - and the European Parliament want to demonstrate their solidarity with Greece as it struggles to hold back the new influx.

Choppy seas

European leaders are desperate to avoid a repeat of the 2015-2016 crisis when more than a million migrants and asylum-seekers, mostly from the Middle East and Asia, entered the EU from Turkey via Greece and the Balkans, straining European security and welfare systems and boosting support for far-right parties among Europeans.

The situation further south in the Aegean Sea was also calmer on Tuesday due to choppier seas, a police source said, after nearly 300 people arrived on the Greek islands by boat from the nearby Turkish coast on Monday.

A Syrian boy died on Monday after he and 47 others were plucked from the sea when their boat capsized. He was the first reported death since Turkey opened its border.

Turkey, which already hosts 3.7 million refugees from Syria's civil war and faces another big influx after an escalation of fighting there, has said it cannot take in any more.

Greece has been infuriated by Turkish President Tayyip Erdogan's claim late on Monday that Greek soldiers killed two migrants and badly wounded a third, something Athens denies.

"When a country uses people as a battering ram, fabricates fake news to mislead them, and systematically violates the sovereignty and sovereign rights of neighbouring countries, it is in no position to point fingers at anyone," the Greek foreign ministry said in a tweet.