Locals in the coastal village of Tafitoala in Samoa say their livelihoods have been destroyed and that they deserve compensation after a New Zealand naval vessel sank there earlier this month.

The area around the wreck of HMNZS Manawanui, off the southern coast of Samoa's most populous island Upolu, has remained closed off as authorities continue to monitor for potential chemical leaks.

Fatu Totua would normally be out on the water fishing with his son, but he has been prevented from doing so since the ship sank a few kilometres from his home in the first week of October.

That has left him without an income.

Mr Totua told the ABC that he and his son would usually earn 200 Samoan talas ($108) per day by selling the fish they caught.

Samoa's Marine Pollution Advisory Committee confirmed to the ABC that "approximately" 200,000 litres of diesel had leaked from the vessel since it sank.

New Zealand Defence Minister Judith Collins told the New Zealand current affairs program Q+A that the figure of 200,000 litres was unlikely to be correct, describing oil coming out of the wreck as "a little trickle".

"Any oil coming out is obviously disturbing for people but we do know that it has not gone to the beaches. It is quite a small amount that we can see," she said.

Asked why Samoa's explanation was different to that of New Zealand authorities, Ms Collins said: "I don't know".

The New Zealand Defence Force said on Saturday: "We cannot definitively state how much fuel has leaked at this time but do consider, based on a week's worth of evidence, that it is probable that the amount of fuel leaked is less than 200,000 litres."

The Samoan government has confirmed that 5,000 square metres of the reef was damaged by the NZ Navy shipwreck and anchor chain.

White Sunday ruined by shipwreck

Over the weekend Samoa marked its national holiday White Sunday, which celebrates the nation's children.

Mr Totua, who has six children, said the lost income meant he was unable to treat his children or properly celebrate the holiday.

Neitina Malae, who hires fales — beach huts — to tourists and visitors, says their livelihood has also been impacted.

White Sunday is usually one of the busiest times for her business with families flocking to the beach. 

But the closures at Tafitoala meant lost revenue for Mrs Malae, who said she felt sorry for other families and children who would not be able to celebrate the festival as usual.

"There will be children without a new outfit for White Sunday because the truth is: those without money during White Sunday are the people of our village Tafitoala, who depend on selling fish," she said.

There has been discussion that some villagers want the Manawanui shipwreck to become a tourist attraction of its own.

But Mrs Malae said she wants the ship to be removed altogether.

Associate Professor Nick Ling from the University of Waikato said that while coral reefs could naturally recover from physical damage, "this process can take many years depending on the scale of damage".

"This can be facilitated by physically reattaching coral fragments. However, this can only be undertaken once debris from the wreck has been removed," he said.

'Nothing but sadness' in Tafitoala since the wreck

Malae Saili would normally be guiding tourists in the area, taking them to do activities such as surfing, kayaking, fishing or watching turtles.

That work has dried up since the Manawanui sank — and Mr Saili wants compensation.

"No-one wants to come here … we had bookings that have been cancelled following the confirmation of the impact on the sea," he said.

"When this incident occurred, it brought nothing but sadness because … so many depend on the sea not just to fish for food but some sell the fish to earn a living."

New Zealand's ministries of Foreign Affairs and Defence did not specifically respond to the ABC's question about compensation, but said they "absolutely appreciate the importance of the marine and coastal environment to local communities and acknowledge their concerns".

"Our focus continues to be on reducing any possible environmental impacts and supporting the response," the spokespeople said.

"It is too early to comment on other issues at this stage. We first need to understand the situation and that will take time."

The New Zealand government has ordered a military court of inquiry to investigate how the sinking occurred.

Ms Collins, the defence minister, last week dismissed the calls of some Samoans for an apology from New Zealand.

"We're obviously deeply traumatised. Frankly, our navy has gone through a very tough time," she said.

"We are dealing with the immediate issues and anything like that, government to government, would be dealt with by the prime minister, if at all."

Afoa Patolo Afoa, who still makes his living as a fisherman at age 76, said the damage to the reef had implications beyond his village.

"Normally we sell fish on Sundays but starting from when the vessel ran aground and sank, the people came but there's no fish."

Mr Afoa said the New Zealand government needed to do more than simply clean up the environmental effects, but also provide financial compensation to residents.