The New Zealand foreign ministry has already hauled in the Japanese ambassador Yasuaki Nogawa for a dressing down over the incident last Friday, which it labelled "unhelpful, disrespectful and short-sighted".
Key said he supported Japan going one step further and issuing an apology over the incursion, which took place when the whaling ship Shonan Maru 2 entered the EEZ as it was chasing the Sea Shepherd protest vessel Steve Irwin.
"We had earlier on made it quite clear our view about the Japanese ship coming into New Zealand's economic zone."
"We'll see what happens from here, but whether there's an apology -- we'll wait and see."
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The foreign ministry said the ship did not enter New Zealand's territorial waters, which extend 12 nautical miles from the coast, but did breach its EEZ, which covers a region 12 to 200 nautical miles offshore.
While the vessel was legally entitled to sail in the EEZ, the ministry said it had been made clear to Japanese officials before it entered the waters on Friday that it was not welcome.
High-seas confrontations are common between Sea Shepherd's protest ships and the Japanese, who hunt whales under a "scientific research" loophole in the moratorium on whaling.
In 2010 a collision involving the Shonan Maru 2 resulted in the sinking of Sea Shepherd's speedboat Ady Gil.