New Zealand’s health minister has been demoted after he ignored national lockdown rules and drove his family to a beach 20km from his home.

Last week Dr David Clark was photographed going for a mountain bike ride 2km away from his Dunedin home. He apologised for the incident, saying it showed poor judgment at a time when all New Zealanders were being urged to stay at home and only exercise in their local area.

Now Clark has revealed a further indiscretion, calling himself an “idiot” for deciding to drive his family 20km to the Doctor’s Point beach on the first weekend of lockdown.

Lockdown rules state cars should only be used to purchase essential supplies such as food or medicine, and exercise should be taken in the local area only.

Clark said the revelation came about as part of his preparation for appearing in front of the epidemic response committee on Tuesday, requiring him to provide prime minister Jacinda Ardern “with a complete picture of my activity outside my home during alert level 4”.

Clark said the beach trip during level 4 lockdown was a clear breach, and he had offered his resignation to Ardern – who had not accepted it.

“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,” Clark said in a statement.

“As the health minister, it’s my responsibility to not only follow the rules but set an example to other New Zealanders … I’ve apologised to the prime minister for my lack of judgement and offered her my resignation.

Ardern responded swiftly to Clark’s revelation, stripping him of his associate finance minister portfolio and demoting him to the bottom of the cabinet rankings.

Political commentators say it is likely Clark will lose the health portfolio when the coronavirus crisis is resolved, and criticised him for failing to show his face regularly or taking on more of a leadership role, leaving that job to Dr Ashley Bloomfield, the director-general of health.

“Under normal conditions, I would sack the minister of health. What he did was wrong, and there are no excuses,” Ardern said in a statement.

“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.”

Ardern said New Zealanders expected their ministers to uphold the rules that they themselves had set, which were trying circumstances for everyone to adhere too.

Under level 4 lockdown, which New Zealanders have been under for nearly two weeks, Kiwis cannot leave their homes except for essential supplies such as food or medicine, and could only take brief bouts of exercise in their local area.

“I expect better, and so does New Zealand,” Ardern said.

Clark is not the only high-profile New Zealander to flout the rules. All Blacks first five Richie Mo’unga has apologised after he was filmed kicking and passing a rugby ball with other professional players at his local park.

“I want to start off by saying this was not an organised training. There were no communications beforehand saying that we should train in this park together. It was by coincidence that I rocked up and they were there training,” Mo’unga said on social media, but the prime minister and NZ rugby have both criticised the meet-up.

Mo’unga went on to say he intended to run around the park alone, but “instinct” made him pick up the rugby ball.

“It’s something that I’ve learnt that even [though it was] my natural instincts, it’s something I need to be more careful of and I will be more careful of.”

Cases of coronavirus have begun to stabilise and decline in New Zealand, with experts saying the country may be the only western nation with a chance of totally eradicating the disease.

“This does suggest that what we are doing as a nation is working,” Ardern said at her daily media briefing.

“We do appear at this early stage to be on track”

Fifty-four new cases of the virus were confirmed on Tuesday, bringing the total to 1,160. One person has died from the virus, an older woman with pre-existing health conditions on the west coast of the South Island.

Twelve people are being treated for the virus in hospital, with four of those requiring intensive care. On Tuesday more people recovered from the illness than contracted it, the director-general of health said, an encouraging milestone.