Suppression around details of the Phillip John Smith case -- pointing the finger at the Prime Minister -- has been lifted.

Specifics of the unsuccessful application to move the matter to the High Court had previously been suppressed by two judges but those orders were lifted in the High Court at Auckland this morning.

Phillip Smith allegedly fled to South America while on temporary release from Spring Hill Corrections Facility in South Auckland on November 6. He was serving a life term at the time for the 1995 stabbing murder of the father of a boy he had sexually abused.

He was caught in Rio de Janeiro on November 13 -- a week after he left New Zealand last year.

In attempting to elevate the case to the High Court, his lawyer Dr Tony Ellis submitted that John Key, Peter Dunne and the Parole Board had all breached his client's right to the presumption of innocence.

Dr Ellis' application also suggested Smith had been unlawfully removed, "abducted or kidnapped" from Brazil.

The lawyer objected to the media's labelling of Smith as a "paedophile" in his bid to have the case moved.

The application to change jurisdiction was rejected and the matter will be back in Auckland District Court in August.

He and his sister Joanne -- who is accused of helping him illegally obtain a passport -- are set to go to trial in January.