The Edinburgh News has reported that the Edinburgh Churches for Sanctuary coalition submitted a 400-signature petition calling on the city to help Syrians.
On Tuesday councillors in Scotland will vote on joining the UK government's Vulnerable Persons Relocation scheme.
Under the scheme, refugees thought to be most in need will be selected by UN agencies for removal to the UK, where they will receive government support for their immediate needs before responsibility passes to a local authority.
It was reported that just over 140 refugees from the country were brought to the UK by the end of 2014.
Almost four million Syrians have fled their homes since the conflict began four years ago and are living in refugee camps in Turkey, Lebanon, and Jordan. Families have fled the fighting between government forces and rebel groups.
It is thought that Christian minorities in Syria have been targeted in attacks. Sarah Kyambi is a member of Grace Church Leith and one of the organisers of the Edinburgh Churches for Sanctuary.
She said the group had come together out of a desire to help suffering Syrian refugees: "We thought that Edinburgh, as Scotland's capital, should be playing a lead role.
"We thought that more needed to be done to respond to one of the biggest humanitarian crises of our time, and we wanted our city to step forward and play its part.
"Our faith teaches us that we should be compassionate towards strangers.
"These people have had to flee their homes, lost their livelihoods and loved ones, and this is something that Edinburgh can and should do."
Church of Scotland minister and Edinburgh Cyrenians chief executive Ewan Aitken helped establish a centre for asylum seekers in the capital ten years ago. He said that the display of compassion was typical of the city: "Edinburgh has always been a place where folk have been made welcome.
"We should always remember that when you reach out to your neighbour, you reach out to yourself. The city has been good at that over the years."
