Hager said the information would show New Zealand was "far more involved than most people realise".
"The discussion about GCSB [Government Communications Security Bureau] in New Zealand has always been about GCSB spying on New Zealanders. What this is going to be about is all the other countries New Zealand spies on.
"Some of that won't be a surprise and some of it will be a great surprise."
Hager said the information would not only surprise the public but also "people all through the foreign policy and intelligence bureaucracy who will know much more about this subject at the end of these revelations than they did before.
"When I read through this material and see that New Zealand is doing these things, it seems bizarre to me - like it is from another era."
The collaboration with The Intercept extends to a series of stories with three newspapers - the New Zealand Herald, the Herald on Sunday and the Sunday Star-Times.
Hager said the collaboration was driven by The Intercept's wish to ensure the material was made widely available.
Whistleblower's greatest hits
Spying on foreign leaders
Edward Snowden revealed the United States had monitored phones of 35 world leaders, including German Chancellor Angela Merkel and Brazil's President Dilma Rousseff. Australia targeted the Indonesian President while Britain's spies were monitoring emails of politicians at two G20 meetings in London.
Cable tapping
The Five Eyes spy partners have tapped into the world's internet and telecoms cables, Snowden revealed, giving it the ability to suck up almost all the data which passes through them.
XKeyscore
The so-called "Google for spies" is a search tool which trawls the massive pool of data acquired by the NSA and its partners. It operates at 150 sites, according to one Snowden document, including one in New Zealand.
Mobile phone encryption
The US and UK hacked into the world's biggest sim card manufacturer, taking encryption keys. It gives the potential to bypass security and listen in on content passing across networks in dozens of countries.
Hack attacks
The NSA's Tailored Access Operations unit can hack info from protected computer systems and is able to install malicious software on computers and phones.