Opposition MP Jamie-Lee Ross says the Prime Minister needs to speak to the Minister of Health following reports David Clark tried to stop staff at Middlemore Hospital from releasing information to media.
Newshub obtained a voicemail and emails which suggest the Health Minister tried to gag senior staff talking publicly about the state of embattled Middlemore Hospital.
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In one case he even appeared to promise a board member, who he'd sacked, another job if they shut up.
Dr Clark denies claims he tried to gag anyone.
While he wouldn't go as far as to say Dr Clark should be sacked, Mr Ross said he needs to be hauled in front of the Prime Minister for a stern talking to.
"I think the Prime Minister should be looking seriously at whether he's followed the cabinet manual - it's her responsibility to keep her Government ministers in line," he said.
Judith Collins agreed, later telling The AM Show while it shouldn't go straight to sacking, Dr Clark needs to front up and tell the truth.
"Let's not jump straight into sacking mode - let's have a look and ask him to come up and front up and be truthful to the public," she said.
Fellow Labour MP Phil Twyford defended Dr Clark, saying the scale of the scandal was being exaggerated by the media and opposition MPs.
"I think you're making a mountain out of a molehill with this thing - there's no evidence of [intimidation] from what I heard. You're putting two and two together and getting five," he said.
Mr Ross accused Dr Clark of outright lies during the scandal, saying he was telling the media he didn't know about issues while senior staff said he did.
"He went into the media and then you've got text messages from Rabin Rabindran saying 'this is the information we gave you, you said you didn't receive the information but we gave it to you'," he said.
"He had to admit later on that he received what he called 'a wodge of papers', but when the CEO wanted to release those very same papers, his office tried to shut him down."
As for whether the scandal will end here, Mr Ross said absolutely not.
"There's a whole lot more to come," he said.
"David Clark has been found out, he tried to shut people down and that's absolutely wrong."