New Zealand's maritime safety authorities says they want the ship moved as quickly as possible before the weather worsens, to avoid any risk of an environmental disaster.
Unable to start its engines, the whaler is restrained between two other vessels, but the Maritime New Zealand organisation remains worried about the prospect of it sinking and releasing 1,300 kilolitres of fuel and furnace oil into the pristine Antarctic environment.
Maritime New Zealand wants the ship to use whatever means possible to get under way, according to reports on national radio.
It said it would allow the ship to enter New Zealand waters if it got into trouble, even though Chris Carter, the conservation minister, has said he does not want a boat full of whale meat, oil and chemicals in one of his ports.
The company which owns the boat has declined an offer by the Greenpeace environmental organisation's ship Esperanza - sent to the area to protest at the whaling operation - to tow it to safety.
A company spokesman said the full extent of the fire damage, which would decide whether its engines could be restarted, would not be known until Monday.
Meanwhile, he insisted the ship posed no major risk to the environment.
The United States coast guard's icebreaker Polar Sea, which went to the area at the request of the New Zealand government, found no signs of environmental pollution in the Ross Sea, Radio New Zealand reported.
The Nisshin Maru is the only ship in the Japanese fleet able to process whale carcasses and the Japanese said the season's whaling expedition would be finished if the ship could not be repaired.
If it had to be taken to a port for major repairs, the rest of the fleet would have to return to Japan.