Oil from HMNZS Manawanui was seen out in the ocean on Monday but there has been none so far on coastal areas, a Samoan government minister says.
The $100 million specialist survey ship, which hit a reef at the southern end of Upolu on Saturday night, sank on Sunday morning.
Navy Commodore Shane Arndell said it was resting 30m under water on a reef off the south coast, and was not leaking.
Samoan transport secretary on the fate of HMNZS Manawanui
Samoa's secretary for transport Fui Tupai Mau Simanu said specialist teams, including divers, were able to go out onto the water for the first time on Tuesday after rough weather eased.
A sweep of 20km to 30km of coastal areas and beaches on the south-west side of Upolu had found no sign of oil.
"Having said that, initial assessments that were done when we were able to fly some drones there on Monday, there were signs of oil ... that was leaking out from the boat when it first went down and it was being pushed out in the swells and it went out into the ocean," he told Morning Report.
Fui Tupai Mau Simanu said he would get a more substantial report from the crews on Wednesday, including damage to the reef and the impact of any leaks.
The Samoan government would be asking for access to information from the ship's black box, he said.
Defence Force diving crews recovered the voyage data recorder - the equivalent of an aeroplane's flight recorder - on Tuesday.
As well as giving the NZDF information on what caused the sinking, it would also "hopefully give us an idea of what we want to do in order to prevent any environmental disaster," he said.
"Ultimately we want to prevent any leakages, because the boat went down with a whole lot of fuel, and that's what we're really really concerned about," he said.
Maritime lawyer on HMNZS Manawanui sinking
Maritime lawyer Sid Wellik said if recompense for any damage was needed, it would most likely be decided by the two governments.
There was a general obligation for a state to make right any damage done to another nation, he said, and in this case the most likely outcome would be a solution through diplomatic discussions that were probably going on already.
On the investigation into the sinking, Wellik said it would be up to the Court of Inquiry to decide what it would make public.
He said courts of inquiry were "unique" in that they were generally private. Any disciplinary action would be a separate process.
"One of the things it may do, it may make a recommendation that disciplinary action is taken however that would be only a recommendation and the the person receiving that recommendation would have to determine whether they take that action and if so in what way."
'It's very bad for New Zealand'
Labour leader Chris Hipkins told Morning Report there were a lot of questions to be answered but reports the evacuation of the ship was well handled were good to hear.
It was a very serious situation and better information was needed but "the more fundamental questions of how we got into this situation are ones that we should take very very seriously".
"It's not great for New Zealand, in fact it's very bad for New Zealand."
It was important the defence force was properly resourced and funded, he said.
"Our defence force has been dealing with some pretty run down equipment, having said that, the current ship Manawanui was one of the new ships that was purchased during that time [of the previous government], so I think there are some fairly big questions about why a relatively new ship, well maintained, found itself in this situation."