Tamihere was jailed for life with a 10-year, non-parole period in 1990 for the murders of Swedish tourists Heidi Paakkonen and Urban Hoglin.
He was released last year after 14 applications for parole. Mr Hoglin's body was found by pig hunters on the Coromandel Peninsula but Ms Paakkonen was never found.
The Parole Board said recent months had been dominated by serious health problems for Tamihere. The board would not say what the health issues were but it was believed to be serious arthritic and cardiac problems.
"He has spent large amounts of time in hospital, and that is disappointing to record, but he says at the moment he feels much better," said the board in its report released after it relaxed Tamihere's parole conditions.
"He has complied fully with the conditions of his release. A special arrangement was made recently so that he could attend the wedding of his son. That was obviously highly successful and well managed."
Tamihere had been on full residential restrictions since his release but the board said it was only a matter of time before he moved to partial residential restrictions which involved a curfew only.
"We think that in view of his excellent compliance, that could happen in the near future."
The board said from June 1, Tamihere's parole conditions would be relaxed to include a 9pm-6am curfew unless he had written approval of his probation officer.
Another special condition was that he did not go to the Coromandel Peninsula, Kopu and Whangamata without his probation officer approval.
Tamihere would be called back before the board in November for another progress and monitoring report when other changes to his parole conditions could be considered.
The board said Tamihere wanted to return to the area of his ancestors and "careful arrangements will need to be made about that. They are being planned at the present time.
"We record however overall an excellent report which shows full compliance and we note that accordingly," the board said.
