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".