With recent media exposure of the extent of mass surveillance by some of the GCSB's (Government Communications Security Bureau) partners in the Five Eyes international intelligence sharing arrangement, public trust in intelligence agencies was at risk if surveillance activities weren't seen to conducted appropriately.
"We believe much of the public's concerns could be alleviated if there was satisfactory oversight of surveillance powers and we propose an independent cross-party select committee to oversee intelligence agencies," the commission said.
But Mr Key dismissed the commission's concerns and criticised the quality of their work.
"I think the Human Rights Commission actually should take a step back and ask themselves the question why they failed to put a submission in on time. They are funded by the Government and they were the only people that couldn't actually make the deadline."
"Actually the bill narrows the GCSB's scope in its current form, it doesn't extend it," he said.
"I actually don't think it was a very good submission at all, and they need to pull their socks up. If they're going to continue to be a government-funded organisation they should meet the deadlines like everyone else did."
Commission spokesman Gilbert Wong said Mr Rutherford's report was not a submission, but the Prime Minister's comments pointed to another misgiving the commission had about the legislation.
The commission could have made a submission, "but there was quite a short period for people to prepare their submissions ... we did seek an extension but that wasn't granted."
"Our position is that the details of how to do so and when this was to occur were not readily available, and the time for making submissions on such important and technical legislation was unreasonably short."
The commission was exercising its statutory ability to directly report to the Prime Minister for only the fourth time since 1993, "because of the seriousness of the proposed bills and to allow for more time to consider the bill's impact."
"It's not something we use lightly but we feel this is something important."
Labour Leader David Shearer welcomed the fact the commission had "underlined what we have always wanted, which is a full and independent inquiry".
The need for that was now urgent, given the speed with which the legislation was being advanced, and "because I think it will restore public confidence in our intelligence agencies, which at the moment is pretty low."
Mr Shearer also said it was "pretty worrying" that with the commission having come out with a view Mr Key didn't like, "there's then a threat about having its funding pulled".
The commission also recommended:
* Stronger accountability and oversight mechanisms, including Parliamentary oversight from a cross-party select committee, in addition to the Inspector-General of Intelligence and Security.
* Amending the bills in line with the submissions of the New Zealand Law Society and the Legislation Advisory Committee.
* Taking into account the submissions of internet New Zealand, particularly as they relate to human rights.
* Human rights training for all members of New Zealand's intelligence services.
Read the full reports here.