However, environmentalists say they are concerned that the vessel could become trapped by moving Antarctic ice.
The Nisshin Maru, which has a load of 500,000 liters of heavy oil and 800,000 liters of furnace oil, is currently lashed to two other whaling ships near the Antarctic coast.
The stricken vessel is about 175 kilometers from the world's largest Adelie penguin breeding rookery.
Japan's government-affiliated Institute of Cetacean Research has rejected offers by Greenpeace and a US Coast Guard icebreaker to tow the ship, saying it was unnecessary.
"At the moment the Japanese are saying 'we can cope'. They'd better be right"
Helen Clark, New Zealand prime minister
Helen Clark, New Zealand's prime minister, said on Monday: "My advice is if you can't see a way of getting that boat out of there without some help either from the American vessel or from Greenpeace or from somebody else, the world is going to be very upset if there's a major spill in that area.
"At the moment the Japanese are saying 'we can cope'. They'd better be right," she told the NewstalkZB radio network.
Steve Corbett, a spokesman for Maritime New Zealand, said the whaling ship was drifting north away from Antarctica.
"They have six vessels there. Between them, they should be able to rig up some sort of arrangement," he said.
Japan's Fisheries Agency said on Saturday that officials had not given up hope of reviving the vessel.
The fleet however may be forced to abort hunting for the remaining season which runs until mid-March if the Nisshin Maru remains inoperable.
The whalers had planned to hunt up to 945 whales but how many have been killed so far is not known.
Japan says its annual whale hunts, begun after the International Whaling Commission imposed a global ban on commercial whaling in 1986, are for research but meat from captured whales are sold as food.
Environmental groups say the hunts are a pretext to keep Japan's tiny whaling industry alive.