Victorians will not be allowed into SA unless they are essential travellers or live within 70 kilometres of the border.

Returning South Australians will also be subject to quarantine requirements and could soon be forced to seek a special exemption, Police Commissioner Grant Stevens said.

Before Sunday's change, only people from Greater Melbourne were barred from coming to SA.

"This is the reality of dealing with a global pandemic. We'll keep doing what we have to do," Mr Stevens said.

The new requirements came as Victoria reported another 19 local virus infections, taking the total number of cases to 43.

Chief Public Health Officer Nicola Spurrier said the risks posed by the outbreaks in both Victoria and NSW was increasing.

"This is the highest risk we have experienced since the Victorian second wave," she said.

"It feels to me we've got a dam and the waters are coming up higher. We've got to have our borders in place."

The border changes also came amid threats of a blockade by truckies angry over new essential worker rules.

The Transport Workers' Union said it was unrealistic to require essential workers crossing the border to have a virus test within 24 hours, which could leave some truckies needing to get tested every day.

State secretary Ian Smith said some freight drivers were already refusing to come into SA and Victorian truckies were threatening a blockade to prevent the supply of food.

"We understand the current circumstances are ever-changing but in order to achieve a relatively undisrupted transport industry there needs to be flexibility, not only from essential workers but also the state government," Mr Smith said.

Premier Steven Marshall said the government had already moved to "massively" increase testing at the border and officials would meet with truckies.

"Our truckies have kept Australia moving during this coronavirus and we're grateful for that," Mr Marshall told reporters on Saturday.

But the premier said the new border rules were "absolutely necessary".

Mr Marshall said there was also a direction in place now which allowed truck drivers to come in with proof of a negative test result in the previous 48 hours.

Mr Stevens said he was confident Monday's meeting with the freight sector would result in authorities and the industry "finding a mid-point".

He said he hoped truckies would appreciate that the steps being taken were in the best interests of all South Australians.

SA reported no new local virus cases on Saturday despite having several hundred people in quarantine over their links to potential exposure sites both in South Australia and Victoria.

All have returned negative virus tests so far, something the premier said was a "positive result for us here in South Australia".

Mr Marshall said it was "miraculous" that a family who relocated from Sydney and spent five hours with virus-infected removalists had still not come down with the disease.

"We're asking those people to stay in directed home isolation for 14 days because we know there is an incubation period so we're not out of the woods yet," the premier said.

"But the early results are extremely good for South Australia. I think we've dodged a bullet."

Australian Associated Press