James is being held in remand while awaiting trial for two charges, including aggravated robbery, and is also facing a charge of escaping police custody. He denies the charges.
Whanganui prison director Reti Pearse told the Chronicle last week that the application for James to be accompanied by Corrections' staff to visit his dad in hospital had been declined.
Mr Pearse said the safety of the community and Corrections staff would be at risk and public safety was his priority.
However, on Wednesday evening, Corrections Chief Custodial Officer Neil Beales said approval had been given for James to attend a private family service outside the prison.
"Given the risk involved, we will be putting increased security measures in place for this," Mr Beales said.
"Our job is to keep communities and our staff safe, and all decisions are made on that basis.
"There were a range of factors that impacted the decision not to allow the prisoner to visit his father in hospital last week.
"He is remanded in custody on serious charges, including aggravated robbery and escaping police custody. The alleged escape occurred while the prisoner was being escorted to hospital."
It was unclear just when James would be allowed out. His father's funeral is scheduled for Thursday in Whanganui, but the family may delay if it means James can attend the service.
The family's story has sparked national attention. James' sister Michelle Taikato tried to contact a number of politicians and deputy Labour leader Kelvin Davis' office had got back to her, she said.
"On Tuesday night I got a phone call from chief custodial officer Neil Beales, and that phone call was due to a push from Kelvin's people."
Ms Taikato said Mr Beales had been helpful and supportive.
Mr Beales passed on his condolences to the family, saying: "This is a very emotional time for the family involved.
" I have talked on several occasions with the prisoner's sister and I want to thank her for her patience and for the information she has provided to us."
Ms Taikato said one of the things the family wanted to come out of this was a new look at prisoners' rights.
"You can look back and judge other people's lives and what they've done, and some people have done some pretty horrific things.
"The consequences of that are prison for a very long time, but I don't think that the consequences should be missing out on saying goodbye to loved ones."
