"John Key only needs to look at rulings from around the world to see that this gross violation of privacy cannot ever be justified.
"The GCSB needs to put a stop to mass surveillance and come clean with New Zealanders about how much spying goes on. We know that the GCSB engages in mass surveillance, yet it is an illegal practice around the world."
Dr Graham said the Green Party had always maintained that mass surveillance did not have a solid legal basis and had to be stopped.
Snowden, who remains exiled in Russia, has also claimed that New Zealand's spies are undertaking mass collection.
Leaked documents revealed the GCSB conducted "full-take" surveillance on Pacific nations, including targeted operations to spy on emails and other communications of politicians.
After the Greens lodged a complaint, the Inspector General of Intelligence and Security Cheryl Gwen launched an inquiry into the GCSB to investigate whether it intercepted New Zealanders' communications while they worked or travelled in the Pacific.