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Medway Green Party is calling on the council to accommodate refugees as the president of the European Union proposes a quota plan for member states.
The party want Medway Council to welcome just 50 refugees and have called the UK's refusal to take more than 20,000 refugees shameful.
A spokesman for the party said: "Helping, even a small number, would be a small step by Medway Council, but make a huge difference to those individuals saved from fear, inhumane living conditions, and possible death.
"What we are asking is for Medway Council to join other Councils in making a declaration that refugees are welcome in our towns and demonstrate practical steps they will be taking to accommodate refugees."
He added: "We feel it is shameful that, as a European country that unilaterally bombed Iraq, we can dodge our responsibility for one of the consequences, and turn the other way, when people are in dire need.
"We call upon the people of Medway and Medway Council to contribute towards the reversal of this trend”.
So far Medway has taken in three unaccompanied minors and no adults, whereas Kent County Council are looking after 720 unaccompanied children seeking asylum.
Leader of Medway Council, councillor Alan Jarrett said: "It is for the government to determine immigration policy and to adequately fund councils which may be affected by any such national policy."
Yesterday, President Jean-Claude Juncker used an annual address to unveil policies to force members of the EU to take a share of 160,000 asylum seekers.
Britain is able to opt-out of the compulsory quota scheme meaning and the government has confirmed it will not be opting in or making any further contribution than the 20,000 refugees it has already said it will take.
The Green Party spokesman said they welcomed the proposals that will take the pressure off the few countries coping with the largest number of refugees, and alleviating the ongoing insecurity for those fleeing their homes.
He added: "It speaks volumes for the need for a continued union of European countries when it comes to dealing with major crises, which frankly could simply be allowed to escalate to genocidal proportions if all acted as our government; turning the other cheek, reinforcing the barricades, conceding only slightly to public reaction when they witness the death of a small child."
The Green Party want all 433 local and county authorities in the country to take in just 50 refugees each, which would amount to a total of 21,000 people overall.
"The UK has a humanitarian responsibility as a country whose actions have helped to create the political and military chaos in the region from which many of the refugees are fleeing," he said.
"We also have a responsibility to our European neighbours who are currently struggling to cope with the numbers fleeing to their shores."
Councils are able to seek help with resettling refugees from National and European funded projects.