Increased oversight was of no benefit if the boundaries of what it could do were blurry.
The GCSB is New Zealand's foreign intelligence agency and Dr Harrison said while the bill had provisions to protect against the interceptions of the "private communications" of New Zealanders and permanent residents, it was not clear what that meant.
He said it certainly did not protect the communications of a commercial company with an overseas party, such as Fonterra communicating with China.
Mr Key is the Minister in charge of the Government Communications Security Bureau.
Other members of the committee are Labour leader David Shearer, Greens co-leader Russel Norman, Act leader John Banks and National Minister Tony Ryall.
The Council of Trade Unions in its submission says unionists have long been targets for surveillance and accusations by security forces and it is concerned about new powers being proposed for the GCSB spy agency.
The CTU concerns were now "acute" given the revelations of commonplace monitoring of electronic and telephonic communications by the United States' National Security Agency (NSA) in the Guardian newspaper after leaks by NSA contractor Edward Snowden.
Council president Helen Kelly is presenting the submission.
Assurances that Mr Key had given that information sharing with overseas intelligence partners (Australia, US, UK and Canada) was not used to circumvent New Zealand law "ring somewhat hollow" because it was unclear how the GCSB had been interpreting New Zealand law.
The CTU wants any changes to law allowing the GCSB to spy on New Zealanders or permanent residents to be postponed until an independent inquiry is held - that is also the position of the Labour and Green parties.
"The CTU has consistently expressed a high degree of concern regarding the increase in powers and intrusiveness of surveillance in New Zealand society," the submission says.
Among the CTU's concerns are what it sees as an increased use of private investigators by companies to watch people it considers are working against its interests "and other developments that could be used against people considered opponents of the government of the day".
The bill is the result of a review of the GCSB prompted by the admission that it had spied unlawfully on internet mogul Kim Dotcom in 2011 to assist with a raid on his Coatesville mansion by the FBI.
The surveillance was unlawful because he was a permanent resident. The review found that 88 New Zealanders had been spied on since 2003.
Recently retired Inspector-General of Intelligence and Security Paul Neazor declared that they were all lawful but said the law was unclear.
The CTU is now calling for Mr Neazor's report to be made public, even if parts of it had to be withheld to protect sensitive ongoing investigations.
"It is important to address public suspicion that he has been 'captured' by the agencies it is his unique role to scrutinise."
Releasing the report would be an important step in that direction.
Mr Key yesterday said former High Court Judge Andrew McGechan would replace Mr Neazor, who has been in the job since 2004.
Today he said former Appeal Court Judge Bruce Robertson would replace Sir John Jeffries as Commissioner of Security Warrants. Sir John has held the post since 1999.
The bill allows for greater domestic spying by the GCSB. It explicitly allows the GCSB to spy on New Zealanders when it is helping agencies such as the Security Intelligence Service (SIS) and the police to perform authorised surveillance activities.
