The family of an Iranian Christian convert imprisoned for her faith are fearing for her life after she refused to end her hunger strike.

Maryam Naghash Zargaran has pledged to continue her protest until she is released from prison.

Speaking to the International Campaign for Human Rights in Iran, Zargaran's mother, Zahra Pour-Nouhi Langroudi, said her daughter "won't stop until the authorities pay attention to her demand".

"She also said she will not accept medical treatment at the prison clinic because the last time she was there the physician... insulted her and called her a liar," Langroudi added.

"I demand my daughter's unconditional freedom. I have been going to the offices of the prosecutor and the Supreme Court every day, but no one gives me a straight answer. They are indifferent. I don't know what else to do for my child's freedom."

Langroudi said her daughter had been suffering from numerous health problems before prison, and they have been exacerbated by the poor conditions and insufficient treatment she has received since being incarcerated in Iran's notorious Evin Prison.

"I'm worried that her hunger strike will threaten her life," Langroudi said. "She underwent heart surgery in 2015 and the doctors said she must avoid stressful conditions, which is impossible in prison."

Zargaran was arrested in 2013 along with pastor Saeed Abedini, who was granted early release as part of a prisoner swap with the US earlier this year.

She was charged with "propagating against the Islamic regime and collusion intended to harm national security" and sentenced to four years in prison.