Europe should brace itself a for a potential "massive" influx of Syrian refugees , a top European Union (EU) official said Wednesday. "We need to be prepared for the possibility of an even more massive influx," internal markets commissioner Michel Barnier said during a European Parliament debate on Syria, Agence France Presse (AFP) reported. A number of EU nations, including Bulgaria and Greece, have reported a strong increase in refugees from the 30-month-old Syrian conflict, according to AFP. More than two million Syrians have fled the bloodshed in their country and sought refuge in neighbouring states - mainly Lebanon , Jordan  and Turkey - and the number of displaced Syrians could reach 3.5 million by the end of 2013 , Barnier cautioned. "The response surely should not be to close national borders, to shrink away or barricade ourselves," said Barnier, speaking as representative for the European Commission, AFP reported."This is not a strictly national issue; it is a European issue.""Any crisis of this size affects us all and we must be ready in a spirit of great solidarity," the official added, AFP said. Following a decision made by EU lawmakers to adopt a resolution calling for a humanitarian aid conference to assist Syria's neighbouring countries with the burden of hosting thousands of refugees, Barnier reiterated his support for the move."We are in agreement on the principle (of the conference) and will have to see how to organize it," Commission spokeswoman Pia Ahrenkilde-Hansen confirmed in Brussels, according to AFP.The UN High Commissioner for Refugees Antonio Guterres  has asked EU nations to offer asylum to 10,000 Syrians and resettle 2,000 of the most vulnerable, AFP reported.Some 50,000 Syrians have applied for protection since the beginning of the conflict in March 2011, mostly in Sweden and Germany .