Officials in New Zealand and environmentalists are concerned about the potential damage if the ship, the Nisshin Maru, spills oil or other toxic chemicals near Antarctica's largest penguin rookery.
"Everyone wants the Nisshin Maru moved as soon as possible … no-one more than Japan"
Glenn Inwood, Japan's Institute for Cetacean Research
The vessel, part of a Japanese whaling fleet, is adrift about 220 kilometers north of the pristine Antarctic coast.
Glenn Inwood, spokesman for Japan's Institute for Cetacean Research, responded to Carter's demands saying "everyone wants the Nisshin Maru moved as soon as possible … no-one more than Japan".
"The sooner they can get the girl [vessel] moving, the sooner they can leave that area of the Antarctic," he told reporters.
Inwood said the best thing to do for the safety of the crew was to get the ship seaworthy again.
He said the crew are checking the ship's radar, autopilot and rudder controls, and continuing to re-wire electrical circuitry damaged in the fire.
The main engine was re-started but had been turned off for the repairs, Inwood said.
However he said the whaler, which is currently lashed between two other vessels from the fleet, posed no immediate threat because the Ross Sea was still calm and the ship was not in any danger from moving ice.