Mr Key said he would not comment further until investigations by the Auditor-General and the Privacy Commissioner were completed.
Mrs Collins refused to discuss Ms Pullar's allegations but issued a statement saying it was a high priority to rebuild the public's trust in ACC.
"I cannot emphasise enough how seriously I view recent privacy-related issues. Privacy and information security are the biggest challenges facing ACC at present," she said. "At this stage, I am not yet satisfied ACC's privacy provisions and protocols are appropriate, or are being complied with to the level they should be."
Ms Pullar also alleged that ACC chief executive Ralph Stewart would have known that no threat was made in the meeting because he had heard the secret tape in its entirety soon after the police complaint was made. He did not reveal this to reporters when asked about the tape last week.
She argued that the complaints were "sideshows" to the organisation's mishandling of her file, serious privacy breaches, and increasingly unfair treatment of long-term beneficiaries.
The Green Party repeated calls for ACC head John Judge to stand down, saying he had overseen the mishandling of files and the programme of removing claimants from its books.
The long-running dispute between Ms Pullar and ACC led to the resignation of ACC Minister Nick Smith from the Cabinet and a legal stand-off between his successor, Mrs Collins, and Labour MPs Trevor Mallard and Andrew Little.