Some 59 members of the European Parliament said in a letter to the European Commission that Greece is breaking the law in its treatment of refugees and called for an end to the violence along the Greece-Turkey border.
Greek troops and riot police remained on high alert on Tuesday along the land border between Greece and Turkey, the main flashpoint in an escalating row between the EU and Ankara over how to deal with a new wave of migrants and refugees.
Tens of thousands of migrants have been trying to breach the border since Turkey said on Thursday it would no longer uphold a 2016 accord with the European Union to keep refugees on its territory in return for billions of euros in aid.
EU foreign policy chief Josep Borrell, along with the EU commissioner for crisis management Janez Lenarcic, will pay a two-day visit to Turkey, the Turkish Foreign Ministry said on Tuesday.
Greek authorities said the border had been quiet overnight, in contrast to the clashes seen over the weekend and into Monday, when police used tear gas against migrants, including women and children, stuck in the no man's land.
"There were only a few attempts today [by migrants to cross the border]. Let's hope they get the message," a machine gun-toting army officer told Reuters 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.
It has sent military and police reinforcements to the area, which have used tear gas and water cannons to repel mass attempts by migrants to cross into the country.
Authorities have also set up cordons of police and army checks on and near the border, arresting those who managed to make it through.
"Greece's borders are also Europe's borders," Greek Prime Minister Kyriakos Mitsotakis said in a statement released ahead of 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 migrant tide.
EU leaders call for end to violence
Some 59 members of the European Parliament said in a letter to the European Commission that Greece is breaking the law in its treatment of refugees and called for an end to the violence along the Greece-Turkey border, rights group Are You Syrious reported.
The move by Greece to shut its borders "is in breach of national, European and international law, including of the principle of non-refoulement," the letter said.
"Greece needs to comply with all national, EU and international laws also in regards of its obligation to provide legal access to its territory and the asylum procedures," the letter continued.
It highlighted that the issue is not Greece's problem alone but Europe's responsibility and "none of us has the right to turn a blind eye."
European leaders are desperate to avoid a repeat of the 2015-16 crisis, when more than a million migrants, mostly from the Middle East and Asia, entered the EU from Turkey via Greece and the Balkans, putting a heavy strain on European security and welfare systems and boosting support for far-right parties.
The situation further south in the Aegean Sea was also calmer on Tuesday due to choppier seas, a police source said, after nearly 300 migrants 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 fatality 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 migrants.