His comments follow scathing comments from some Supreme Court judges in their ruling this month that such surveillance was illegal.
"The deliberate unlawfulness of the police conduct in the covert filming ... is destructive of an effective and credible system of justice," wrote Chief Justice Dame Sian Elias.
The bill will be introduced today and sidesteps the Supreme Court decision by making covert video surveillance lawful. It has been tweaked to ensure it does not give police broader powers than they had before; courts would still have the ability to rule camera use unlawful if it breaches the Bill of Rights Act protection against unreasonable search and seizure.
The committee will report to Parliament on Monday and the House will go into urgency next Thursday to pass the remaining stages of the bill.
One of the issues that continues to be challenged is whether the bill needs to be retrospective.
Labour leader Phil Goff said he was cautious about retrospective legislation: "I'd be reluctant to do it unless there was very strong evidence that serious alleged criminal offenders would get off the hook.
"Having urgency and retrospective effect is getting worst of both possible worlds."
Mr Key said that it was possible to drop the retrospectivity.
"But that would have an impact on the 40-odd trials we want to bring to court. There are also potentially issues from people who have been convicted taking an appeal."
The Attorney-General, Chris Finlayson, said: "It is necessary for the avoidance of doubt, because otherwise you'd have quite a few challenges to the lawfulness of evidence."