Clashes have broken out between police and Greeks protesting against the government’s measures against the influx of refugees.

On Saturday, some 500 demonstrators marched through Greece’s northeastern town of Kastanies, situated on the frontier with Turkey, to express their anger at a border fence in the region that spans over 10 kilometers (6.2 miles).

Police tried to stop the protesters from crossing the border and fired tear gas at them.

Chanting "No borders, no nations," the protesters also lit flares and attacked the police.

Greece's Prime Minister Alexis Tsipras had on Friday said that he was “ashamed” to be the premier of a European Union member state, which has been shirking its responsibility for properly dealing with the current refugee crisis.

The criticism came while Greece completed its border fence with Turkey in December 2012. The fence forced asylum seekers to change their route from Turkey to Europe and take dangerous journeys to reach the continent.

Refugees board a dinghy to the Greek island of Chios from Cesme in the Turkish province of Izmir, October 31, 2015. ©AFP

Athens has resisted calls to demolish the controversial border fence with Turkey, with Greek Migration Minister Yiannis Mouzalas recently saying that “at this stage - for purely practical reasons - ... the opening of the border fence is not possible.”

Officials in the European countries reportedly remain divided over how to deal with refugees, most of whom are fleeing conflict-hit zones in the Middle East and Africa.

While some European leaders support an open-door refugee policy, others are in favor of controlling the EU's external borders, deporting more people and paying third countries to keep asylum seekers on their soil.

According to the latest figures released by the International Organization for Migration (IOM), 724,228 refugees have reached Europe’s shores so far this year while a total of 3,329 people have either died or gone missing in their perilous journey to the continent.