The Green Party is calling on Prime Minister John Key to seek the support of all the parties in parliament for any proposed changes to the laws governing the intelligence and security agencies.
An independent review of the Security Intelligence Service and the Government Security Communications Bureau is in the hands of the Intelligence and Security Committee.
It is due to meet on Tuesday to discuss the review report and decide when it will be released, which could be later this week.
Mr Key has said it is "highly likely" that the government will propose law changes as a result of the recommendations in the report.
"I'll be very reluctant to move forward if we can't get Labour's support on the legislation," he said at the end of last month, when the committee received the report written by Sir Michael Cullen and Dame Patsy Reddy.
Green Party co-leader Metiria Turei says law changes that could impact on the privacy of New Zealanders should have wide political support.
"The government should seek the support of all political parties if it is to change any laws following the first regular review of New Zealand's security and intelligence agencies," she said.
"Currently the Intelligence and Security Committee is a closed shop, with neither of the major parties being particularly strong on civil liberties or human rights."
The laws covering the GCSB were re-written in 2013, and the legislation said there would have to be a review of the legislation around both agencies in 2015.
The purpose of the review was to discover whether the legislation is adequate for the agencies to carry out their functions.
Mr Key hasn't revealed the review's findings, but says he met its authors before it was completed.
"There's a general perspective that the SIS legislation at the moment is not fit for purpose and there are areas where they can see improvement in the way they can work together [with the GCSB]," he said last month.
Mr Key is chairman of the committee and his nominated members are Chris Finlayson, the minister in charge of the SIS and the GCSB, and Justice Minister Amy Adams.
Labour leader Andrew Little is an automatic member, and he nominated David Shearer.
The committee is set up after general elections.
The Greens were part of it in the previous parliament when Labour nominated one of their MPs, but Mr Little decided to have Mr Shearer, and the Greens were shut out.