School closures and stockpiling a fortnight’s food to prepare for coronavirus self-isolation are “premature” for the general population, the health minister, Greg Hunt, and chief medical officer, Brendan Murphy, have said, though all options are on the table.

Appearing alongside Hunt on ABC’s Insiders on Sunday, Murphy said that federal authorities are currently recommending that returned travellers socially distance themselves although others should begin “practising” to do the same, especially at-risk groups such as the elderly.

Both reiterated these settings may change in future, with Hunt confirming that all options are on the table in the event a more general lockdown is required.

Public concern about the consistency of advice about responding to coronavirus has grown as schools and universities prepare for shutdowns and the Victorian chief medical officer has suggested stockpiling a fortnight’s worth of food.

Labor and medical experts who do not report directly to governments have suggested Australia has been too slow to roll out a public information campaign and to advise in favour of more drastic social distancing.

On Friday the Council of Australia Governments agreed that from Monday non-essential gatherings of more than 500 people across Australia should be cancelled.

Scott Morrison said the advice did not apply to attendance at work, childcare, schools, university lectures, public transport, airports “or things of that nature”.

On Sunday Hunt told Insiders the government’s best estimate is that the coronavirus will reach its peak in Australia in a “six-month window” although it “might be longer”.

Asked about general lockdowns, Murphy replied they may be used although they may focus on one part of the country and not others.

“It – it is potential that could be the case,” he said. “But that may be focal. One of the things we know about outbreaks of infections is that they can affect one part of a country, not another.”

Asked if Sydney could be locked down and not the rest of the country, Murphy continued: “Potentially you could. The Koreans did that for two provinces, very successfully locked them down. Everything is up for consideration.”

“There are no options that are off the table,” Hunt said. “The paramount goal, and the prime minister said this to me at the outset, is protecting health.”

Murphy said authorities were “strongly suggesting that returned travellers should practise what we call ‘social distancing’.

“So that’s keeping a distance of 1.5 metres, if possible, from people, not getting in close contact … not shaking hands [and] avoiding all public gatherings.”

Murphy said that advice relating to gatherings of 500 people or more “may well change” but Australia, which he said had “only 250 cases”, was still “ahead of the curve”.

“If you’re over 70 you should be more careful, particularly if you have chronic disease, you should … [exercise] more social distancing,” he said, and “avoid things that aren’t essential”.

Murphy said for others the risk of attending public places with fewer than 500 people, such as a cinema, was still at this stage “relatively low” and at the moment authorities were not recommending people stop taking the train. As case numbers increase, the medical advice will respond to recommend greater social distancing, he said.

“I think the gym is fine but everybody at the moment needs to practise very good hygiene.

“If you’re going to the gym, I would be very focused on hand washing, using hand sanitisers, all of those social distancing, good hygiene measures, we want everybody in the community to start practising those.”

Asked about the Victorian chief medical officer’s suggestion people should stockpile a fortnight’s worth of food, Murphy replied it was “a little bit premature at the moment”.

“For most people we don’t want to encourage major panic buying at the moment – we’ve seen that with the supermarket chains. But I think it is probably sensible to have a few days of supply.”

Asked about school closures, Hunt said the government was keeping all options on the table and would be guided by medical advice.

He said governments did not want to “move too early” because of the risk of children being at home with their grandparents and “taking parents out of the workforce who might be in the health and medical sector, [and] disrupting supply chains”.

Murphy said there was “no question we have a range of social distancing measures that we will not hesitate to recommend to government but they’ve got to be proportional and they might last for a long time”. “So you don’t want to move too early.”

Murphy said there were “very few reports of symptomatic infection in children” and authorities don’t know “whether children are getting infected but just don’t get symptoms [and] they can still spread it or they’re not getting infected”. “The former is probably more likely.”

Murphy also suggested children getting infected may contribute to herd immunity.

Hunt said the government had started rolling out its first information campaign about coronavirus, and advice can be accessed at health.gov.au. The campaign urges people to wash their hands frequently, cover coughs and sneezes, and dispose of tissues, and avoid contact with others if they’re feeling unwell.

Murphy said Australian authorities define “close contact” – which requires self-isolation – as “someone who has been in contact with someone who is symptomatic at any stage or up to 24 hours before”.

He then clarified that only people with contact with someone with coronavirus who had symptoms in the last 24 hours needs to self-isolate because they are “very, very unlikely to have been infectious”.

On Sunday Bill Bowtell, adjunct professor at the Kirby Institute for Infection and Immunity, said he was “aghast” at the lack of clarity and structure in the coronavirus response.

Bowtell told Sky News that Murphy’s advice on hand shaking was “inconsistent with what New South Wales Health is saying” and argued there is “no coherent advice” about whether schools should open from Monday.

Bowtell said the government appeared to “have no plan” for the fact people whose wages are at threat will be unlikely to get tested, and said it was “imperative” to address the issue. The Morrison government has trimmed the waiting period for sickness allowance by one week, but rejected calls to introduce paid leave for casuals.

Earlier, Hunt and Murphy addressed the revelation on Friday that the home affairs minister, Peter Dutton, had been infected with coronavirus, after attending cabinet on Tuesday.

Murphy suggested commonwealth offices in Sydney may have been cleaned out of an “abundance of caution” and Hunt suggested Qantas may have contacted passengers near Dutton on an earlier flight because the time period had not been determined.

Hunt said Queensland Health had now determined “the relevant time for contact with Peter Dutton was the 11th of March”, meaning cabinet members did not need to self-isolate as a result of Tuesday’s meeting.

On Friday Coag agreed to weekly meetings of a “national cabinet” made up of Morrison, the six premiers and two chief ministers, as well as key federal ministers such as the treasurer. The first meeting will be held at midday on Sunday.

So far Australia has responded to the coronavirus through travel bans from the worst-affected countries, a $2.4bn health package to create 100 fever clinics and boost telehealth consultations and a $17.6bn stimulus package to prevent a major economic downturn.

The Morrison government has set up a new coronavirus business unit in the Treasury to support business confidence, employment and business continuity.