The move follows the hard closure of the border between the two states, which led to 312 people rushing across the border from Victoria into South Australia between 6pm and midnight last night.
Premier Steven Marshall said that all people who have been to Victoria in the past couple of weeks will be asked to present themselves for a test, regardless of whether they have symptoms or not.
Anybody returning to SA in the coming days will also be required to take a coronavirus test within 24 hours of their return and again on day 12.
They will be handed free face masks and a pre-signed COVID-19 test referral form at the airport or border check-points, with SA Health to telephone all arrivals within 24 hours to check that they have been tested.
New arrivals will also be required to self-quarantine for two weeks, with police to ramp up surveillance checks to ensure people are properly isolating at home.
To assist with the testing blitz, the State Government will from from next week roll out a fleet of mobile COVID-19 testing vans, which will be stationed in areas that are currently not serviced by one of the 50 permanent testing clinics already in operation across SA.
Marshall said the surge in virus infections in Victoria is a “stark reminder of why we need to remain vigilant”.
He said the increase in testing clinics and pre-signed referral forms meant there was “absolutely no excuse” for people arriving in South Australia to not be tested.
“It’s a blunt reminder. We can’t rest on our laurels,” he said.
But Health Minister Stephen Wade said South Australia had stopped short of imposing mandatory testing, describing such a move as “completely pointless”.
“What is of concern is that 14-day incubation period – that’s why we’re asking people to be tested on day 1 and on day 12,” he said.
Meanwhile, Australian Defence Force personnel are currently mobilising to help SA Police monitor “secondary roads” on the Victorian border.
The ADF will also assist police in the state’s operations centre in Mount Gambier from today.
SA Police Commissioner and state emergency coordinator Grant Stevens said it was unknown how many ADF personnel would be deployed to South Australia.
“When we seek to use the Defence Force we have to be confident that this is a necessary step and there are no other measures that would be feasible in the short term,” he said.
“The reality is, with the number of crossing points that we have, particularly down in the southeast, it is a significant challenge to police all of those opportunities.
“Based on our assessment the Defence Force was the best way to go.”
Stevens said he “expected” that he would request a further 28-day extension to the state’s current major emergency declaration, which ends on July 25.
From Thursday, only people returning home from Victoria and essential travellers are allowed to cross into SA.
So far, 31,000 people have applied for pre-approval travel exemptions into South Australia.
Of those, 6000 are classed as “essential travel”, 5000 are from people arriving from states and territories where South Australia has lifted its border restrictions and a further 3000 requests were ordered to self-quarantine.
The new restrictions apply to everyone arriving by road or air, while people living in cross-border communities will be restricted to a 50km radius inside SA.
Stevens said maps were being produced to clearly show the entry limits and anyone from Victoria found breaching the rules could face a $1000 fine or further action.
People living near the border and needing to enter SA to conduct daily activities, such as attending school or for work, must have a pre-approved essential traveller exemption.
South Australia reported no new virus cases on Thursday and no longer has any active infections.
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