European Union justice and interior ministers have started urgent discussions on how to tackle the migrant crisis amid the stream of new arrivals and continuing disagreements over how to seal off borders.

Monday's meeting comes days after EU President Donald Tusk warned that Europe's passport-free travel area, known as Schengen, could break apart if the migrant strategy is not sorted out within two months.

Ministers will be seeking to stem the flow through Greece, where authorities are struggling to contain the crossings by boat from Turkey.

Belgium's interior minister, Jan Jambon, says that Greece "has to do what it has to do — namely, controls. And if that is not the case, we need to look closely into that."

EU figures show more than 2,000 people are still arriving daily.