Health Minister David Clark has been demoted after driving his family 20km to a beach to go for a walk in the first weekend of the lockdown - a breach that the Prime Minister says he would normally be sacked for.

"At a time when we are asking New Zealanders to make historic sacrifices I've let the team down. I've been an idiot," Clark said in a statement this morning.

Jacinda Ardern said he would be demoted to the bottom of the Cabinet rankings and stripped of his Associate Finance portfolio.

Clark, who offered his resignation, sounded forlorn as he started a round of media calls this morning, saying he felt "like a complete dick to be honest".

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And speaking to Newstalk ZB's Mike Hosking, Clark said he "wasn't thinking" when he drove to the beach with his family.

His wife had asked him if it was within the rules, and he had decided to go because the family would still be within its household bubble.

"I make no excuses for it, Mike. I got it wrong," Clark told Hosking.

"I've made a fool of myself. I need to be really clear on that and apologise to New Zealanders."

He said the Health Minister in the middle of a global pandemic was an incredibly important role, and he had a long way to go to rebuild the trust of New Zealanders.

Former Police Commissioner Mike Bush said before the first weekend that people were not allowed to drive to the beach.

Clark has already come under fire for driving about 2km last week to go for a mountain bike ride.

Ardern said: "Under normal conditions I would sack the Minister of Health. What he did was wrong, and there are no excuses.

"But right now, my priority is our collective fight against Covid-19. We cannot afford massive disruption in the health sector or to our response. For that reason, and that reason alone, Dr Clark will maintain his role."

But Ardern said he would pay a price for breaking the rules.

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"While he maintains his Health portfolio, I am stripping him of his role as Associate Finance Minister and demoting him to the bottom of our Cabinet rankings.

"I expect better, and so does New Zealand."

Health Minister David Clark speaks to Mike Hosking after being demoted for breaking lockdown rules.