Nearly 200 people have signed a petition asking Babergh District Council to accommodate ten Syrian refugee families.
The petition, one of 19 initiatives across Suffolk, was published by online campaigning organisation 38 Degrees.
It was presented to the council on Tuesday evening.
The incoming families would be among those admitted to the UK through the Vulnerable Persons Resettlement Scheme, and will come directly from camps in Lebanon.
Rosemary Loshak, who initiated the petition, said it was independent of party affiliation.
“I was motivated by shame and frustration at the government’s minimal response to the unfolding humanitarian disaster,” she said.
“Compassion is a universal trait and it has been heartwarming how readily many have told us of their concerns as they came forward to sign.
“I understand since I began it has become likely that refugee families will be allocated to Suffolk in the near future.
“We hope now to put together a group of volunteers to welcome families in conjunction with Suffolk Refugee Council, the churches and other agencies.”
The petition was received by district councillor Jan Osborne, portfolio holder for Health, Wellbeing and Communities.
The Government will provide financial support at least for the first year and to assist in finding accommodation. Individuals will be able to work or claim benefit according to their circumstances.
On Tuesday it was also announced that Suffolk Public Sector Leaders unanimously agreed to support the Syrian Vulnerable Person Scheme when they met on October 16.
Leaders felt Suffolk should offer to take up to 200 Syrian refugees via the scheme.
A spokesman said that due to the location of suitable housing, health, education and support services the refugees will be settled mainly in the greater Ipswich area.
Jennie Jenkins, chairman of Suffolk Public Sector Leaders and leader of Babergh, said: “We have agreed we should play our part in providing accommodation and support to some Syrian refugees.”
Anyone wishing to assist Ms Loshak in supporting the refugees should contact her by texting 07831 574575.