Australian Medical Association president Tony Bartone says it is time for a comprehensive nationwide shutdown, including closing schools and any sectors not actively fighting coronavirus.

Dr Bartone said too many Australians were disregarding existing rules, while mixed messaging from governments had brought confusion and anxiety.

“It’s clear from all the data that we do need to – because of the lack of consistent messaging, because people have been flouting the earlier advice regarding social distancing measures – that we need to move further and more quickly to ensure that whatever we’re seeing around the world doesn’t mimic and occur in our front doors,” Dr Bartone told the ABC on Thursday.

The AMA calls on governments to adopt deeper physical isolation measures. Only those people essential to defeating #COVID_19 should now be at work #covid19australia #coronavirusau #auspol https://t.co/04V150irT6

— AMA Media (@ama_media) March 25, 2020

Dr Bartone’s call for more action came as Australia’s coronavirus death toll rose to 12 on Thursday.

The latest deaths are 68-year-old Garry Kirstenfield, from Toowomba, and three Victorian men in their 70s, who died on Wednesday and whose names have not been released.

At 3pm on Thursday (ADST), there were 2793 COVID-19 cases across Australia.

However, deputy chief medical officer Nick Coatsworth has come out strongly to combat criticism the federal authorities have been too slow to restrict movement and the spread of the coronavirus in Australia.

Dr Coatsworth said the effectiveness of ramping up social isolation restrictions was “a contested point”.

Echoing comments from fellow deputy CMO Paul Kelly on Wednesday, he said there were “two schools of thought” about how to respond to the outbreak.

“The experts around the table of the Australian Health Protection Principal Committee do not think that this will be over in weeks if you put in harder and faster measures. So, this is about degrees. We’ve gone hard and fast,” he said.

Dr Coatsworth referenced ABC health journalist Norman Swan as putting forward a view at odds with the AHPPC.

“I disagree with Norman [Swan] when he thinks that this is going to be over in weeks if we go for harder and faster lockdowns,” Dr Coatsworth said.

“I would like Norman to go to Darwin and tell the people of Darwin why they have to stay in their houses when we’re a continent and there’s differential expression of this virus and its impact across the country.”

“We’ve gone hard and fast. To say that we’ve gone light and slow would be completely inaccurate. The measures that we’ve got in at the moment are unprecedented.”

– Deputy Chief Medical Officer, Dr Nick Coatsworth pic.twitter.com/7pPzMVivI7

— News Breakfast (@BreakfastNews) March 25, 2020

Australian doctors have been demanding the federal government close schools and non-essential workplaces to contain the spread of coronavirus.

“The virus has been always one step ahead of government in terms of the demand and the requirements,” Dr Bartone said.

Dr Bartone acknowledged that some jurisdictions around the world had not closed schools and managed to have lower and flatter curves than Australia.

However, “we also know that they have had much more significant measures when it comes to social isolation and managing the community spread of COVID-19,” he said.

• Related: What Australia’s frontline healthcare workers need you to know now

On Wednesday, Australia’s chief medical officer Brendan Murphy said whether or not the government brought in stricter measures depended on how seriously Australians took the current arrangements.

But Australian Society of Anaesthetists president Suzi Nou warned the health system would not cope with a massive spike in demand unless more was done to flatten the curve.

“We must drive behaviour, and we must move early,” Dr Nou said.

“Every day without drastic action from now is likely to result in a more severe and extended crisis, owing to the cruel mathematics of pandemic.”