David Littleproud will write to eBay to ask them to clamp down on “parasites” who appear to be selling hoarded groceries online and says Australia is at no risk of running out of food.

The agriculture minister said a lack of trust in government and traditional media sources had contributed to the waves of panic buying, leading to people trusting false reports of lockdowns and shortages on social media.

“It is obviously being exacerbated by misinformation on social media,” he said. “Most Australians are calm, I think. But when they see an essential of life is not on the shelf where they are used to it being, that obviously creates a vacuum.”

Littleproud engaged in a media blitz, including writing in Guardian Australia, to reassure a panicked public that Australia produced three times the food needed to feed its population and to urge people to return to their normal shopping habits so that the supplies have time to reach the stores.

“We have enough food … it’s just about making sure that supply chains continue,” he said.

He said the Australian government’s response to the coronavirus crisis had been based on the advice of the commonwealth, state, and territory chief health officers – “experts, not politicians” – and that if people had faith in the government, supermarkets, and Australian farmers, the shortages would be resolved.

“I think social media will kill this country,” he said.

Major supermarkets Coles, Woolworths and Aldi have placed restrictions on a number of products and repeatedly pleaded with customers to return to their pre-pandemic shopping habits and to stop abusing supermarket staff.

But, more than three weeks after it began, the hoarding of food and groceries in response to fears about the coronavirus has continued apace, creating a lag in the restocking of supermarkets that has left some shelves bare and caused yet more panic. Some regional supermarkets have started checking the identification of prospective shoppers to make sure they have not driven out from a city.

If shoppers stopped buying more than they needed, Littleproud said, the problem would swiftly be resolved.

“If people are calm and go back to their normal shopping habits then the shops won’t run dry … [and] we will have one less problem to worry about,” he said. “We are expending a lot of energy and time on a problem that we should not have to deal with.”

Australia produces enough food to feed 75 million people per year and has a population of 25 million.

Littleproud said he believed some of the shortage was due to the “parasitic” behaviour of people who were buying supplies and selling them online, and said he would write to eBay to ask them to crack down.

Earlier, the home affairs minister, Peter Dutton said he was “going after” people who he suspects of profiteering from concerns around the coronavirus, telling 2GB he had asked the Australian Federal Police, Home Affairs, and various state police to investigate.

Guardian Australia has asked state and federal police what offences might have been committed by the alleged purchase and resale of goods in Australia, but is yet to receive a response.

The supermarket supply chain was one of the items on the agenda of a meeting of agricultural ministers conducted via teleconference on Thursday, which also discussed the possibility of getting Australian airlines to fly cargo planes to ensure export lines for horticultural products remained open, and the availability of seasonal workers.

Littleproud said he was negotiating with cabinet colleagues on a “tweaking of the visa conditions” of the 140,000 backpackers and 8,000 Pacific Island nationals who are already in Australia, to ensure the horticultural industry has enough workers to pick fruit.

The meeting took place before prime minister Scott Morrison announced that Australia would close its borders to non-residents from 9pm on Friday.

National Farmers Federation president Fiona Simson said she hoped agricultural workers could be made exempt from the lockdown.

“We would definitely be working to make sure that if there are exemptions for essential sectors, that agriculture is considered an essential sector,” Simson said. “If we can work out some way with quarantine requirements that they can enter Australia and carry out their 14-day self-isolation on the place where they are going to work, we would hope there was a provision made for that.”

Simson said she hoped similar exemptions could be made to state quarantines, if other states followed Tasmania in introducing domestic border controls.

Littleproud said he hoped some Australians who had lost work due to the pandemic would seek seasonal or permanent work in the agriculture sector. But he acknowledged many would not be in a position to leave their city or town.