In their first TV interview, David and Wendy Farnell said 'no parents want a son with a disability'.
But in a further twist to the extraordinary saga, Gammy's surrogate mum Pattharamon Janbua claimed that Mrs Farnell wasn't actually the boy's biological mother at all.
She claims that the Chinese-born Australian didn't supply the implanted egg which led to Gammy and his twin sister Pipah being born.
Ms Pattharamon's claims were made after the Farnells sat down for an interview with the Nine Network's 60 Minutes last night (Sun).
They said they had learnt of Gammy's condition too late to terminate and now wanted him back.
Mr Farnell said: "If it would have been safe for the embryo to have been terminated, we probably would have terminated it."
And he denied the couple had abandoned the baby, saying: "I don't think any parent wants a son with a disability. [But] no, we never abandoned him. No, we never said to the surrogate mother to have an abortion.
"We didn't give up on him. The surrogate mother wanted to take our girl. And we were scared we were going to lose her. So we had to try and get out of there as fast as we could."
The separation of six-month-old Gammy from his twin sister, called Pipah, has made headlines around the world and fuelled concerns about the oversight of international commercial surrogacy.
It was then revealed that Mr Farnell, 56, had a history of child sex offences.
Asked whether he was fit to be a father, Mr Farnell, said he 'hangs my head in shame' over his crimes but no longer had sexual urges towards children.
He said: "I am not going to harm my little girl. She [Pipah] will be 100 per cent safe because I know I will do everything in the world to protect my little girl. I have no inclinations ... They have 100 per cent stopped. I don't have this urge to do anything anymore."
Mr Farnell was jailed in 1997 for sex offences involving three girls aged five, seven and 10 from the early 1980s to 1993.
He has three children from a previous marriage and is now married to a Chinese woman, Wendy Li, whom he met through an online dating service in 2004.
She said she had always known about her husband's offences but stood by him and did not believe he would ever harm their daughter.
She said: "He is a good husband, a good father, a very, very good son."
The hour-long interview appeared only to add to tensions between the couple and 21-year-old Ms Pattharamon.
After learning that Mr and Mrs Farnell wanted to seek custody of Gammy, the mother of two, claimed that the egg used in the fertilisation process was not supplied by Mrs Farnell but belonged to another Thai woman hired by the surrogacy agency.
She told Fairfax Media: "Yes, the sperm came from [Mr Farnell] but the egg did not belong to the Chinese woman.
"They are not really related with the baby ... I am not really sure they will give real love to Gammy's sister."
Ms Pattharamon said she has held back revealing Ms Farnell was not the biological mother 'because I didn't want to hurt people' but now feels pressured to speak out after the couple told 60 Minutes they wanted to bring Gammy back to Australia.
But on 60 Minutes, Mr Farnell said the couple fled Thailand with their daughter because they were worried that Ms Pattharamon was planning to keep her.
He said: "We miss our little boy. She [Ms Pattharamon] said that if we try to take our little boy, she's going to get the police and she's going to come and take our little girl . . . and she's going to keep both of the babies."
Mr Farnell said he sometimes returned home from work to find that his wife had dressed their daughter in blue because she wanted to remember Gammy.
Mrs Farnell said: "We miss him every day. We just want to get our son but we don't know who can help us."
The whole tangled saga plays out here.