EU Council President, Donald Tusk, said on Tuesday that even with Greece out of the Schengen-zone, the refugee crisis will not be solved.
After meeting with Greek Prime Minister, Alexis Tsipras, in Athens, Tusk said that the external borders of Europe need to be better protected.
Central European nations suggested an emergency plan to reduce the refugee influx entering Greece from the Balkans.
"The migration crisis is testing our union to its limits," Tusk said.
"For all those talking of excluding Greece from Schengen, thinking this is a solution to the migration crisis, I say no, it is not."
Greece has been under great pressure, as refugees enter the country, most of whom are crossing the Aegean from Turkey.
Last year, more than one million undocumented refugees entered Greece, many on boats. Hundreds also lost their lives on the brisk waters, in an attempt for a better life, however European partners are putting pressure on Greece to increase boarder security.
EU ministers have given Greece up to three months to fix its border security, as failing to do so will result in EU members -of the Schengen-zone- can thoroughly check Greece’s borders, for up to two years.
"Let me be clear," Tusk pointed out.
"Excluding Greece from Schengen solves none of our problems."
Greece said that the number of refugees is too big to cope with, while it said four out of five registration refugee centres are already setup.
The economic crisis Greece is going through, having already a third bailout it its pocket, makes the country struggle even harder, when it comes to the refugee crisis and how to handle the influx crossing into the country.
EU leaders will meet this week to discuss the refugee crisis as well as other EU related issues.