Health Minister David Clark has offered his resignation following a breach of the Alert Level 4 lockdown.

On the first weekend of the Alert Level 4 lockdown, David drove his family about 20km from their house in Dunedin to Doctor's Point Beach for a walk.

"This trip was a clear breach of the lockdown principles of staying local and not driving long distances to reach recreation spots," he says in a statement released this morning.

"As the Health Minister it's my responsibly to not only follow the rules but set an example to other New Zealanders.

"At a time when we are asking New Zealanders to make historic sacrifices I've let the team down. I've been an idiot, and I understand why people will be angry with me."

David has apologised to the Prime Minister for what he says is his lack of judgement and has offered her his resignation.

"In the interest of full disclosure, since the lockdown began I have also driven my family to a walking track about 2km from our house for a walk and gone for occasional runs, all of which were local and within the rules, and one bike ride which is already in the public domain."

Jacinda Ardern says under normal circumstances she would sack David.

She says 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 he does need to pay a price. He broke the rules.

'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."