Opposition parties are blaming Prime Minister John Key for the Government spy agency's illegal eavesdropping.
Mr Key has ordered an inquiry, and says the Government Communications Security Bureau (GCSB) acted unlawfully when it helped police arrest internet tycoon Kim Dotcom and three of his associates.
The prime minister is responsible for the GCSB and NZ First leader Winston Peters says he has failed to oversee its activities.
"This failure... is a dereliction of duty," Mr Peters said.
"Mr Key's shoddy handling of this issue seems to indicate that we are in the pocket of US intelligence agencies and that he allowed them to trample over New Zealand law."
Mr Dotcom is facing internet piracy and money laundering charges in the US, and police were working with the FBI when he was arrested.
Labour leader David Shearer says the GCSB reports directly to Mr Key and has "apparently illegally spied on people involved in the Kim Dotcom case".
"This is a shocking breach of New Zealand's very strict laws restricting the ability of our spy agencies to snoop on people," he said.
"He is responsible as prime minister for signing off all intercept warrants by GCSB."
Mr Shearer is questioning Mr Key's statement after Mr Dotcom was arrested, when he said he hadn't heard of the German internet tycoon until he was briefed the day before the police raid.
"While it has been revealed that some bugging was done illegally, it's not credible to think that other monitoring by the agency was not signed by the prime minister before the raid was carried out," Mr Shearer said.
"This isn't about national security. This is about John Key's own word and whether he has told the truth to New Zealanders."