The converts were named by Barnabas Fund only as Rahimullah and Rita, who have three children, Mohammad and Aisha, who have two children, and sisters Shazia and Sunita.
They fled to India after converting to Christianity but now face being deported back to Afghanistan after India rejected their applications for refugee status.
The converts are afraid they will lose their lives if they are made to return home.
We believe that if we return to our country, our lives will be in danger of death, said Mohammad and Aisha.
In their appeal application to the United Nations High Commission for Refugees (UNHCR), Rahimullah and Rita wrote: As we are converted and baptised Christians, we are deeply fearful for our lives.
In the light of the situation in Afghanistan, we will be sentenced to death and executed by the government or we could be stoned and burned by the people.
Barnabas Fund is appealing for urgent intervention by the United Nations High Commission for Refugees on behalf of the six converts in India.
Dr Patrick Sookhdeo, International Director of Barnabas Aid, said: "The cases of these six dear brothers and sisters highlight the fact that Afghan converts to Christianity are safe neither inside nor outside the country. It is a disgrace that they have been denied refuge when their very lives depend on it.
"I am greatly moved by Shoaib's letter, which demonstrates his tremendous courage in the face of the death penalty. It underlines the urgent need for the international community to press for both his and Said's release, and for the Afghan government to allow true religious freedom."
Christians have come under increasing threat in Afghanistan in the last year after a parliamentarian made a public call for their execution following the TV broadcast of a documentary which showed pictures of Afghans being baptised.
One of the converts identified in the programme was Said Musa, who was sentenced to death and spent months in prison, where he claims he was physically abused by guards. His release was negotiated by the US and Italy over several months.
Another convert, Shoaib Assadullah, remains in prison. He described conditions in a letter smuggled out of prison.
I am undergoing severe psychological pressure. Several times I have been attacked physically and threatened to death by fellow prisoners, especially Taliban and anti-government prisoners who are in jail, he wrote.
Assadullahs case is due back before the courts soon and he expects a death sentence.
The court's decision is most definitely going to be the death penalty for me, because the prosecutor has accused me under the Clause 139 of the criminal code which says, 'if the crime is not cited in the criminal code, then the case has to be referred to the Islamic sharia law,'" he wrote.
Barnabas Fund recently launched a petition and letter-writing campaign to save Afghan converts to Christianity. People are being asked to write to their political representatives highlighting the threats to converts in Afghanistan.
They are also being urged to write to the UNHCR to ask that the failed refugee applications of the six in India are reconsidered.
Find letter templates on the Barnabas Fund website at: www.barnabasfund.org Christian Today