SYDNEY (AFP) - Vigilantes in some Australian outback towns have reportedly slashed tyres of those fleeing coronavirus hot spots in the big cities, according to a government minister who urged calm on Friday (March 27).

Remote areas in the north-eastern state of Queensland are being inundated with travellers - mostly retirees - trying to escape the highly infectious disease, Agriculture Minister David Littleproud said.

"As the borders are being shut, we are seeing a surge of grey nomads from southern states, and also from south-east Queensland, go to south-west Queensland to hide from the coronavirus," Mr Littleproud told Seven News.

"Unfortunately this action could turn caravans into the cruise ships of the outback if someone is infected and spreads it in small communities."

Easter is normally prime season for tourism in Queensland's west, as retired travellers visit the outback and remote areas of the state in droves.

Visitors' vehicles had their tyres slashed in some small towns as panicked residents fear their health systems may struggle to cope with the epidemic, Mr Littleproud said.

"I understand the concern of these people in these communities," he added.

The number of confirmed Covid-19 cases in Australia passed the 3,000 mark on Friday, with the vast majority of infections in major east coast cities such as Sydney, Brisbane and Melbourne.

Queensland, Tasmania, Western Australia, South Australia and the Northern Territory have all closed their borders to residents of other parts of Australia in a bid to choke off the spread of the disease.

But some areas are pushing for tighter restrictions within states, including far north Queensland, where much of the country's mining and food production is based.

"Quarantining North Queensland isn't about playing politics, it's about saving lives," outspoken North Queensland senator Bob Katter tweeted on Thursday.

"If North Queensland goes down, so does nearly 10 per cent of your fruit and vegetables, and a quarter of your mining industry goes down with it," he said in an earlier statement.

Australian officials have repeatedly urged people to avoid travelling as confirmed cases of the virus climb.

"This is not holiday break season," Queensland Premier Annastacia Palaszczuk said after announcing the border closures on Wednesday. "This is the season to stay at home with your family."