The Green Party says the Prime Minister needs to be upfront about whether the Government has hired a private company to spy on New Zealanders.
The party claims that data mining company Palantir has New Zealand Government contracts and wants to embed an analyst inside the Government.
Former CIA employee Edward Snowden revealed last week that America's National Security Agency uses a clandestine surveillance operation known as Prism to monitor computer and telephone networks world-wide.
Green Party co-leader Russel Norman says Palantir has been implicated in that scandal. In Parliament on Wednesday Dr Norman asked the Prime Minister whether Palantir had contracts with the New Zealand Government.
John Key replied that it was not in the public interest to discuss the operational capabilities or contracts of the New Zealand intelligence agencies.
The Greens want New Zealand to offer Mr Snowden refugee status, but Mr Key said he would not be welcome.
Mr Snowden has been in hiding in Hong Kong, but has not been seen since checking out of his hotel on Monday.
No Prism used on my watch - Ferguson
A former director of the Government Communication Security Bureau says the spy agency never used information gathered by Prism under his watch.
Questions have been raised about what data the GCSB had access to since the disclosure of the US surveillance system.
Sir Bruce Ferguson told Radio New Zealand's Nine to Noon programme that his staff never cooperated with Prism. However, he was not able to confirm whether or not anyone knew of the existence of Prism.
Sir Bruce said if the GCSB had ever received information from the US that it could not have actively got itself legally, it would have been destroyed.
More time sought for submissions on spy bills
Several technology organisations have written to Prime Minister John Key seeking an extension for submissions on two surveillance bills.
Five organisations, including Internet NZ and the Telecommunications Users Association, say they need more time to assess how the revelations over Prism could affect the Telecommunications Interception Capability and Security Bill and the Government Communications Security Bureau and Related Legislation Amendment Bill.
The latter bill allows the bureau to legally spy on New Zealanders.
Submissions are due to close on Thursday, but the groups say submitters must now consider issues such as the interception of customer data and the sharing of data by surveillance agencies.
Internet NZ acting chief executive Jordan Carter told Radio New Zealand's Morning Report programme on Wednesday that extending the submission date would not delay the process and ensure that the best input was received.