Health Minister David Clark says he offered the acting chair of the Counties Manukau District Health Board what he calls a "dignified exit" from his role.
He has also denied National's assertion that he attempted to gag a senior health official and tempted him with offers of employment.
In late March, Dr Clark accused the board of keeping him largely in the dark about buildings so badly compromised they may need hundreds of millions of dollars spent on repair or replacement.
Hospital executives said they had warned the minister.
It has since become clear from documents issued under the Official Information Act that the board had told the Health Ministry about the problems.
In early April, Dr Clark put on notice acting chair Mr Rabindran and the head of the board's audit, finance and risk committee, Mark Darrow.
The two have since been replaced.
In a voicemail in mid-April, Dr Clark told Mr Rabindran that he intended to signal publicly that he would consider him for further appointments.
The minister went on to say the main issue, of underfunding in the health sector, was being obscured.
Dr Clark today rejected National MP Jami-Lee Ross's characterisation of that as him trying to gag a health board leader.
"Anyone who listens to the full recording will hear that I was being nothing other kind and gracious towards Rabin Rabindran and offering him a dignified exit from his role as acting chair of the DHB," the Minister said in a two-line statement today.
"This Government is absolutely focused on fixing the problems at Middlemore for patients and staff. That's why I'm focused on working with the new leadership at the DHB to ensure patients get the high quality care they deserve."
Mr Ross, the National MP for Botany, said the Prime Minister needed to call Dr Clark to account.
"David Clark needs to front up to the Prime Minister and the Parliament and explain why he's been doing this," Mr Ross said.
"When the district health board wishes to defend their own reputation and the board chairman, who was also texting David Clark saying, 'There is information out there that is wrong about me, I need to protect my reputation, you need to stop saying these things about the district health board', he shouldn't have a voicemail left by a Minister of the Crown saying, 'Hey, this media coverage is unhelpful, but by the way, there might be some jobs down the line in the future'."
Dr Clark begins the two-minute long voicemail on 18 April saying he wished to give Mr Rabindran an update on timelines, and that there was a "draft" media release he hoped to get to him the following day.
"One of the things I'd like to be able to say, probably not in the release itself, but as a signal - and I think you and I covered this previously, is that I would consider you for further appointments because I think that sends the message that this has been about you, and more about I need to have a refresh in a reset and so on."
"It just sends a different message to say that I will, ah, it might be that I've spoken with you and you're willing to consider other appointments. Of course, you would have to be comfortable with that," Dr Clark said.
"So, I'd just like to test that with you, whether that's something you would be interested in having signalled.
"The other kind of general thing to say is I appreciate the challenge with the media speculation, and I notice more and more getting reported that is really not helping at all, and I'm hopeful that there won't be much more commentary.
"My fear is that if you and I keep commenting, the story keeps ticking along and it becomes about personalities rather than the history which both you and I have inherited. And I would rather not have that distraction about who said what when, when the bigger issue of course is the issue around the historic underfunding of the health sector and the consequences of that."