The New Zealand Defence Force cannot provide a timeline for the removal of the fuel tanks from the Manawanui.
The navy vessel sank after hitting a reef in Samoa in early October.
Commodore Andrew Brown told Morning Report although the priority was removing the fuel tanks, the Defence Force (NZDF) cannot comment on when that will happen.
The NZDF was in discussions with its insurance company, and it "would be inappropriate for me to comment on on timelines and who's paying," he said.
NZDF also could not provide a timeline for the next steps in removing the Manawanui from the reef.
"The team are working through the options. Recovering the vessel is but one option," Brown said.
On Tuesday, three containers from the ship were removed from the reef.
"The containers were a priority ... because they were moving on the reef," Brown said.
"Removing the containers was complex and it took four days to do."
Concerns have also been raised about the risk of fuel leaking from the ship hand damaging sea life.
Earlier this month people on the southwest coast of Upolu in Samoa were told not to eat the fish from the ocean in front of their homes because of the leaking fuel tanks.
It is estimated that about 200,000 litres of diesel has leaked from the shipwreck - although NZDF disputes that figure and says less has leaked.
The NZDF continued to monitor the sheen, but has "not received any reports of any fuel coming ashore," Brown said.
"To date, we've had no reports through the hotline with respect to any impact on fish from via the hotline at all."