The New Zealand embassy made it very clear New Zealand did not want members of the Japanese whaling fleet entering its EEZ, Mr McCully said.
The ship reportedly entered the EEZ but did not enter New Zealand's territorial waters.
"While the Japanese whalers' decision to ignore New Zealand's strong wishes in this respect has no legal implications, clearly it was deeply disrespectful."
The Foreign Ministry had conveyed to the Japanese Embassy in Wellington the deep disappointment of the New Zealand Government that Japanese whalers had been insensitive to the views of New Zealanders by entering the EEZ against New Zealand's wishes.
''This week, I shall take further steps to ensure that the Japanese Government understands how deeply the actions of Japanese whalers' have caused offence," Mr McCully said.
Green Party oceans spokesman Gareth Hughes said the Government should lodge a formal diplomatic protest.
"It is offensive that Japanese whalers are in New Zealand waters."
Capt Chakravarty, who is on his fifth campaign for Sea Shepherd and his third Antarctic campaign, said from Dunedin's X/Y shed wharf - where Steve Irwin was berthed from early yesterday until about 4pm - there had been a "big step up in aggression" during the whaling season campaigns.
The Sea Shepherd vessels had put the Japanese scientific whaling expeditions under the spotlight, he said.
"They're [the Japanese vessels] getting frustrated and are coming at us hard."
That was leading to collisions and a recent nine-hour campaign in which harpoon ships crossed the bows of two Sea Shepherd vessels 86 times, towing a 300m-long steel cable, he said.
In Dunedin for less than 24 hours to refuel and restock food supplies, Steve Irwin was to head back to the Ross Sea to find the whaling fleet.
Capt Chakravarty believed Shonan Maru was "acting as a shield" for the fleet and reporting to factory ships the Sea Shepherd boat's position.
The New Zealand-based spokesman for Japan's Institute of Cetacean Research, Glenn Inwood, said the Japanese did not comment on where their boats were and, given the Sea Shepherd's continuing violence on the high seas, including "deliberate acts of ramming", it was important the Japanese monitored the group's vessels and their whereabouts.
Vessels had a rite of passage and access into other countries' exclusive economic zones and before the "violent harassment" committed by the Sea Shepherd group, Japanese vessels respected requests to remain outside the exclusive economic zone, despite having a legal right to enter.
"The public need to understand that the Japanese must defend themselves to ensure the safety of their crew and vessels," Mr Inwood said.
If Sea Shepherd ships, which sailed under a Dutch flag, were refused entry to New Zealand and Australian ports, Japanese vessels were unlikely to need to enter either country's exclusive economic zone, he said.
Mr McCully said he had been advised Shonan Maru 2 had travelled for some distance inside New Zealand's exclusive economic zone, but stayed well clear of New Zealand territorial waters.
"The seas within the New Zealand EEZ, between 12 and 200 nautical miles, are not New Zealand territorial waters.
"The New Zealand Government has no legal means of excluding any vessel from entering. By contrast we have some legal capacity to exclude vessels from within our territorial waters, 12 nautical miles from the coast."
