"What we need is to prepare the governance of the whole Schengen area to be able to face and address these challenges, to secure our citizens while also having free movement," EU Home Affairs Commissioner Ylva Johansson said.
The European Council President also assured Greece that Brussels would not abandon the country.
The EC has urged the country to do more to protect the EU's external border.
Business leaders say changing the country's liberal immigration policy could cost it $11 billion a year.
The country joins a growing number of European nations that have erected fences in an attempt to contain the continent's migrant crisis.