"While the Japanese vessel has a right to pass through our EEZ, it is disappointing a request not to do so was ignored."
Mr McCully said he did not expect the vessel to enter New Zealand's territorial waters, which extend 12 nautical miles from the coast.
Green Party oceans spokesman Gareth Hughes said it was "offensive" that Japanese whalers were in New Zealand waters. He called on the Government to lodge a formal diplomatic protest.
"Murray McCully needs to do more than just express disappointment; he needs to send a strong diplomatic message to Japan that their whaling vessels are not welcome in New Zealand's waters."
The Steve Irwin's captain, Siddarth Chakravarty, said the Japanese ship was making a mockery of New Zealand's request to stay out of the EEZ.
"We urge Minister McCully to uphold New Zealand's strong stance against the Japanese whaling fleet's operations and demand that the whaling security vessel leaves New Zealand waters immediately."
The New Zealand-based spokesman for Japan's Institute of Cetacean Research, Glenn Inwood, said vessels had a right to enter other countries' waters.
He said Japanese vessels had respected the request to remain outside New Zealand's waters before the Sea Shepherd group's "violent harassment".
However, the Japanese needed to defend themselves to ensure the safety of their crew and vessels.
"In light of Sea Shepherd's continuing violence on the high seas, including deliberate acts of ramming, it's important that the Japanese monitor the group's vessels and their whereabouts."
Mr Inwood said it was unfortunate the Sea Shepherd group was allowed to refuel and resupply its vessels in New Zealand and Australia. If its ships were refused entry, then Japanese vessels were unlikely to need to enter either country's EEZ.
Once the Sea Shepherd vessel Steve Irwin finishes refuelling in Dunedin, it will head back out to the Southern Ocean to rejoin the anti-whaling protest.
Meanwhile, Sea Shepherd claims the Japanese harpoon ship Yushin Maru No. 3 briefly entered the Australian whale sanctuary near Macquarie Island, within Australia's EEZ, while tailing the protest ship Bob Barker last night.
If confirmed, the half-hour incursion could be in breach of a 2008 Australian court injunction that declared Japan's whaling operation to be in violation of Australian law, the group said.