National leader Todd Muller has labelled Health Minister David Clark "the very definition of a non-essential worker".
It comes after Mr Clark was criticised for pointing the blame for border blunders at Director of Health Ashley Bloomfield, while Dr Bloomfield was standing nearby.
The pair were facing the Health Select Committee together yesterday, and answered questions from media afterwards.
The Health Minister was asked if he took responsibility for border failures which included two people who tested positive for Covid-19 travelling down to Wellington from Auckland before being tested, and a number of people having left managed isolation without undergoing tests.
"The Director-General has accepted that protocols weren't being followed, he has accepted responsibility for that and has set about putting it right," Mr Clark said, as Dr Bloomfield stood behind him.
"The Director-General has already acknowledged that the system didn't deliver here."
Mr Muller said the treatment of Dr Bloomfield was "a disgrace".
"He humiliated a man we have grown to respect and trust during lockdown."
Mr Muller also said that Mr Clark should not avoid taking "responsibility for the furore".
"For Ardern, when things go wrong, the buck stops with the frontline workers, never her Ministers, never herself."
Last week, Prime Minister Jacinda Ardern called the border blunder an "unacceptable failure" of the system and brought in the military to oversee isolation and quarantine.
Asked if the public's trust in the Government's response had been damaged, Ms Ardern said Dr Bloomfield had also acknowledged "what we have seen in the last two days absolutely has upset the public, and rightly so".
When asked if she would apologise, Ms Ardern said that she felt "huge remorse that this has happened".
"But I am making sure that we are fixing the system. If I had any personal responsibility for what happened here, of course I’d take that. But my job is to lead, I wear that and I keep going."
Mr Muller has steered clear of criticising Dr Bloomfield. After Dr Bloomfield took responsibility for the errors at the border last week, Mr Muller was asked if the Director General had let Mr Clark down.
"Well, the whole system has let the country down and the accountability for the system to be followed... sits with the Minister of Health and the Prime Minister.
Previous criticism of Dr Bloomfield has not been met well with the public, after former National Party leader Simon Bridges accused him of attempting to control information flow in early May.
Dr Bloomfield has taken responsibility for the border issues and apologised.