Mr Key continues to maintain that is untrue and has released declassified documents he says prove Greenwald was talking about a now abandoned cyber security plan that involved tapping into the Southern Cross international data cable.
Mr Key pointed to Inspector-General of Intelligence and Security Cheryl Gwyn's statement yesterday that she had "not identified any indiscriminate interception of New Zealanders' data in my work to date".
"It's pleasing to have someone that's completely independent of the political process coming out very clearly and very strongly saying there is no evidence to support there has been mass surveillance by the GCSB of New Zealanders," Mr Key said. "I hope New Zealanders will accept my word on it because it's absolutely correct ."
He said Ms Gwyn had powers to "see under the covers" of what was happening with New Zealand's spy agencies, but not what other countries did.
"We've always said there are other agencies around the world that either legally as a result of their own laws, or illegally will be out there potentially collecting information on New Zealanders.
"I'm not aware of that but there always could be."
Asked whether he could rule out mass surveillance of New Zealanders by the NSA he said: "I don't run the NSA any more than I run any other foreign intelligence agency.
"I don't believe they are. There's a long-standing agreement that we don't spy on each other and I'd be absolutely stunned if they were."
Mr Key has acknowledged that any mass cyber-security or mass surveillance programme covering New Zealand would involve accessing the Southern Cross cable.
While the GCSB cyber-security project saw a "probe" built to do that, it was never turned on, Mr Key said on Sunday.
Asked whether the NSA may have tapped the cable itself, he said: "I'm not aware of that".
He pointed to Southern Cross chief executive Anthony Bruce's statement that any suggestion the cable had been tapped was "total nonsense".
But Greenwald yesterday said the NSA had tapped into underwater fibre optic cables around the world without the managers or owners of those cables knowing.
"These ... agencies have all kinds of sophisticated capability to tap into fibre optic cables without being detected and that's been proved ..."
Mr Key acknowledged that Snowden's claim that New Zealanders data were held on XKeyscore was probably true.
PM's stories 'shameless'
US journalist Glenn Greenwald says Prime Minister John Key's defence against his claims of mass surveillance of New Zealanders has been unprecedented in its "shameless" shifting of stories and "blatantly false claims".
Greenwald, who has reported on mass surveillance issues around the world over the past 15 months, left New Zealand yesterday after a week that has seen him clash frequently with Mr Key.
Yesterday he told the Herald: "Of course there have been many governments who dislike the reporting, lots of governments who have denied certain of our claims, but I have never seen a government so shamelessly switch stories from one day to the next and make claims that are so blatantly false with such contempt for the citizenry as the New Zealand Government has done in response to this reporting."
Greenwald believed the Government's strategy has been to hope that "the people will just throw up their hands in confusion and just walk away".
He hoped that beyond the election people "realise there are very serious questions ... and the conflicting claims about it and will investigate it and get to the bottom of it".
