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New Zealand's domestic spy agency, the SIS, and its foreign spy agency, the GCSB, will be the subject of an independent review in 2015 and an automatic review every five to seven years after that.
But Labour and New Zealand First, who wanted a more immediate review, last night remained adamant that they would oppose the bill, and it will pass with a majority of just one.
The Greens called the changes cosmetic and will also oppose it.
Other announced changes yesterday will require the GCSB to be more transparent about the number of warrants and access authorisations it gets each year, with an annual public declaration.
Every time it gets permission to spy on a New Zealander, the Inspector-General of Intelligence and Security will have to be told. And the GCSB will be required to declare the number of times it helps the Police, the SIS or Defence Force with its specialised interception equipment.
If the Government wants to expand the domestic agencies that the GCSB will be able to help, it will have to get the support of Parliament for another amendment bill, rather than Cabinet just ticking it off via regulation.
The annual financial and public hearings for the financial review of the GCSB and SIS will be before the Intelligence and Security Committee.
Difficulties around the term "private communications" which were highlighted by the Legislation Advisory Committee and the Law Society will be reviewed under Mr Dunne's deal in a bid to get consistency across the GCSB law, the SIS law, and other relevant legislation such as the Crimes Act and the Search and Surveillance Act.
Prime Minister John Key said yesterday he believed that the changes addressed many of the concerns raised by submitters on the bill.
Mr Key also declared yesterday that the GCSB did not engage in the mass collection of metadata and that under the bill any collection of metadata of New Zealanders would require a warrant to be approved - by himself and the Commissioner of Security Warrants.
"On the best advice I have had, I believe there has been no mass collection [of metadata]."
He said he would make a fuller statement about it during the bill's second reading.
Mr Key does not anticipate urgency being used to pass the bill through its remaining stages.
"Our view with the GCSB legislation is there's a balancing act here between national security and doing our best to keep New Zealanders safe, and the privacy of New Zealanders," he told reporters.
He understood that events such as Edward Snowden's leaks and Wikileaks changed the political appetite and the political landscape.
The Government Communications Security Bureau and Related Legislation Bill expands the legal power of the GCSB to spy on New Zealanders.
The bureau's empowering legislation prohibits it from spying on New Zealanders but it has done so 88 times since 2003, mainly in helping other domestic agencies.
The amendment bill will explicitly allow it to do so now, and it will also allow it to intercept the communications of New Zealanders in its role as the national cyber security agency.
Act leader John Banks has secured a change to get a set of principles written into the bill including the requirement for the GCSB to have regard to the Bill of Rights Act 1990, which protects New Zealanders against unreasonable search and surveillance.
- Audrey Young of the New Zealand Herald