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The Department of Conservation is appealing to the public to report sightings of the whale.
''We want people to let us know if they see the entangled whale and we will attempt to disentangle it from the rope if we can,'' Doc coastal Otago conservation services manager David Agnew said.
''We have a specialist team of Doc staff trained in whale disentanglement techniques who will travel from Kaikoura to attempt to cut the line ... if it's safe to do so.''
Doc was concerned about the rope causing injuries or impeding the whale's movements.
Mr Agnew said the rope was wrapped around the 12m-long whale's body, across its back behind the blowhole, disappearing below the pectoral fins.
The procedures for cutting whales free from entanglement could take several hours and required favourable sea conditions, he said.
''Anyone who sees the whale shouldn't attempt to cut the rope.
''It's dangerous and can make it more difficult for the specialised team to carry out the disentanglement procedure for freeing the whale.
''Boaties should also take care not to get close to the whale or do anything else that could disturb or harass it as this would also make the team's job harder.''
Mr Agnew said humpback whales migrate south at this time of the year, travelling up to 100km a day, and there would be limited chances to intervene once it was south of New Zealand.
Anyone who saw the whale was asked to report it to the department's emergency number 0800DOCHOT - 0800 362-468 or Doc's Dunedin office (03) 477-0677.