Two Syrian refugee families are due to arrive in Oxford this month.
A pilot scheme to house 10 families fleeing the war in Syria was announced in September and Oxford City Council submitted a bid to the Home Office to trial the plans.
The council announced on Friday two families will he housed in private rented accommodation in the next few weeks.
However, according to city council spokesperson Dominic Llewellyn-Jones, the system put in place by the Government has led to only two families coming to the city.
He said: “Initially it will be two families that will be coming to Oxford. Our original proposal was for 10 families but we understand that it wasn’t possible.”
A petition with 2,467 signatures was presented to a full Oxford City Council meeting on Monday in Oxford Town Hall.
Addressed to all six Oxfordshire local councils, it asks them ‘to give shelter, support and a fair hearing to refugees and asylum seekers in our community’.
City council leader Bob Price said: “The council takes this petition on board and promises to do as much as we can for these refugees that are fleeing persecution.
“The city has a proud history of welcoming refugees, and we have been working closely with Asylum Welcome and City of Sanctuary alongside other agencies in preparing to welcome and resettle them.”
The council unanimously voted to make the recommendation to the council’s executive board to address the petition.
Green councillor David Thomas called for a summit to take place involving all of Oxfordshire’s councils.
However, Cllr Price rejected the recommendation, stating: “No. I don’t think a summit would be helpful.”
The accommodation costs are to be recovered from the Government.