The Bakhsh family are afraid they will be killed by Islamic extremists if they are sent back to Pakistan where Christians are persecuted.
The petition was started by Rev Linda Pollock, the pastor of Possilpark Parish Church in Glasgow where the family worships.
Rev Pollock told Premier she is amazed at the amount of support they have received and has high hopes for the petition to make a difference.
"I'm surprised on one level," she said. "I didn't think we would get above 20 [signatures]. But another level I'm not surprised because this is God's work and it's important that this is acknowledged as God's work. And God is a God of surprises, always."
Maqsood Bakhsh, his wife Parveen and their sons have been seeking asylum in Glasgow since 2012.
The catalyst for the move was the murder of two Christians who were gunned down outside a court, while in police custody, in the Pakistan city of Faisalabad in July 2010.
Mr Bakhsh claims the people responsible for their deaths know exactly who he is and would kill him and his family if they had the chance.
But the Church of Scotland said the UK Government has repeatedly rejected the family's plea for asylum, largely because officials do not believe they would be at risk in Pakistan where blasphemy carries the death penalty.
The family have now exhausted the appeal system as it stands and face turning to the courts if they can raise money for legal costs.
Right Rev Susan Brown, Moderator of the General Assembly of the Church of Scotland said: "Tens of thousands of people want their names to count in the campaign to allow the Bakhsh family to stay in Scotland.
"This is a family who call this country home and the uncertainty they are living with is cruel."
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