It also shows the GCSB was briefed on an NSA program which say backdoors installed into computer hardware allowing its spies easy access into networks.
The information was released with the publication of No Place To Hide, a book by journalist Glenn Greenwald, who broke the Snowden story.
Mr Carter said the documents raised concerns about the level of New Zealand's involvement.
"The latest leaks appear to show that the GCSB was shown X-Keyscore, the data harvesting software; that New Zealand was advised that there was spying on leaders of 'allies' and that the NSA was putting backdoors into company's systems. What New Zealanders deserve to know is whether New Zealanders took part in any of those activities."
Mr Carter said other Five Eyes countries were engaged in debate about the extent of government surveillance and it was time for a similar debate in New Zealand.
"When the GCSB and TICSA Bills were passed last year, there were a lot of angry voices. Since then, tensions have died down. We think New Zealanders are ready to have a mature conversation about the relationship between privacy and security in the Internet era.
"Whatever New Zealand's involvement in particular Five Eyes programmes, the broader question of pervasive monitoring needs to be tackled. It risks reducing the use people can make of the internet, and reducing the gains that can accrue from its rollout. Trust is vital in allowing online social and commercial interaction, but pervasive monitoring - whether by governments, corporates or criminals - puts those prospects at risk."
Mr Carter said the "pervasive monitoring" had led the internet communities to exploring ways to thwart surveillance. He said the Internet Engineering Task Force, which develops technical Internet protocols, was attempting to design ways to make monitoring much more expensive or infeasible.
The Prime Minister has refused to discuss the revelations, saying they deal with operational details. The GCSB would not comment.