The U.N. High Commissioner for Refugees on Tuesday urged European Union countries to stop "bickering" over the new wave of refugees and look at the root causes of displacement instead.
"Frankly, instead of bickering about who takes who or rather who doesn't take whom because that's the main bickering, states should look at the root causes of this," he added, saying that few, if any, of those arriving were in fact from northwest Syria, where fighting has escalated in recent days.
The heads of the three main EU institutions - the executive Commission, the European Council, which represents national governments, and the European Parliament - were due to visit the land border area with Greece's prime minister on Tuesday.
Grandi praised Turkey, which is already hosting some 3.7 million Syrian refugees, saying it had been "very good" at hosting them.
The number of migrants leaving Turkey to cross to Greece via its northwestern border in Edirne reached 130,469 as of 9:15 p.m. local time (0615GMT) Tuesday, Turkish Interior Minister Süleyman Soylu said.
He urged EU member states to give more resources and support to Greece as it faces a new wave of migrants and refugees from Syria and other parts of the Middle East.
"Greece is an EU member state so its primary source of support is European resources," Filippo Grandi told journalists in Geneva. "Greece needs more of that. That is very clear."
Turkey, which already hosts some 3.7 million Syrian migrants, more than any country in the world, says it cannot absorb another refugee wave.