Crew member Fernando Pereira was killed when two French secret service agents planted two bombs on the Rainbow Warrior which was moored in Auckland.
It would be up to police to decide whether to investigate a former French spy who recently confessed to bombing the Rainbow Warrior, Prime Minister John Key says.
However, Mr Key said there was no remaining tension with France over the bombing, which took place more than 30 years ago.
"I think it has been accepted largely what has happened is not that contested now from what I can see, and in the end, like all these things that happen sometimes in life you have to try and put them behind you," Mr Key said.
"Theoretically, if there was to be any follow-up from that it would be a matter for the police to determine whether they believe if there was a case that they would want to pursue."
Mr Key was speaking after the Sunday programme on TV One broadcast an interview with Jean-Luc Kister, who confessed to planting both bombs on the hull of the ship.
Kister also apologised to the family of Portuguese photographer Fernando Pereira who was killed in the explosion, as well as to Greenpeace and the people of New Zealand.
Kister - who spoke with his face uncovered in the hour-long interview - said he believed now was the right time to say sorry.
"Thirty years after the event, now that emotions have subsided and also with the distance I now have from my professional life, I thought it was the right time for me to express both my deepest regret and my apologies," he said.
On July 10, 1985, the Rainbow Warrior was docked in Auckland on its way to protest against French nuclear testing at Mururoa Atoll, about 1200 kilometres southeast of Tahiti.
Kister was working for France's spy agency, the DGSE, which carried out an unprecedented mission to stop Greenpeace by bombing a peaceful protest ship without warning in the waters of a friendly nation.
"I have the blood of an innocent man on my conscience, and that weighs on me," a visibly emotional Kister said in the interview.
"We are not cold-blooded killers. My conscience led me to apologise and explain myself."
The former secret service agent was tracked down by journalists from TVNZ and he told them the mission was "a big, big failure".
The bombing, which killed Pereira, rocked New Zealand and shocked the world. It was state-sponsored terrorism and those who carried it out were never properly held to account.
Alain Mafart and Dominique Prieur, who acted as a support team, were the only two caught of a dozen agents. They were sentenced to 10 years' jail but were both back in France within three years.