The documents emerged in a reporting project between the Herald on Sunday, investigative journalist Nicky Hager and the US news site, The Intercept, which had access to Snowden's information.
But Mr Key said: "I would not take everything these guys say literally by any stretch of the imagination."
He said he had not seen all the information that Hager had access to.
"[Snowden's] a thief and he stole and you've got a bunch of people who've been out there propagating information that's actually been proven to be incorrect."
Mr Key said no country in the world, including China, talked about the work their foreign intelligence gathering services performed.
"They don't do it in the United States ... they don't do it in China, they don't do it anywhere else.
"In the end we have legally established foreign intelligence gathering services - they are there for a reason, they are there for the protection of New Zealand and New Zealand interests and that's what we do."
A Chinese Embassy spokesman told the Herald on Sunday: "China is concerned about [the] relevant report. We attach great importance to the cybersecurity issue.
"We will firmly safeguard our security interests and continue to guarantee our cyber and information security with concrete measures."
An April 2013 document said the plan had verbal approval - the same month Mr Key was in China pledging New Zealand's friendship to the country's president Xi Jinping.
But it was unknown if the plan went ahead because, as sign-off was being sought, whistleblower Snowden walked out of his job with a trove of secrets.
GCSB acting director Una Jagose would not discuss the plan or say if it went ahead.
Green Party co-leader Russel Norman accused Mr Key of "recklessly" and "pointlessly" damaging New Zealand's relationship with China.
"Breaking international agreements to spy on Chinese diplomatic communications in Auckland is reckless. It would bring very little, if any, benefit to New Zealand. If discovered and exposed, it carries enormous economic risk," Dr Norman said.
