Authorities fear there could be undetected community cases of coronavirus in South Australia linked to the outbreak in Victoria.
Fifty-one local cases have now been linked to the cluster which has plunged Victoria into a seven-day lockdown.
SA Health has sent more than 50,000 text messages surveying the movement of recent incoming travellers from Victoria.
Just 22,000 people have replied, with about 1500 placed in quarantine after attending known exposure sites.
SA's chief public health officer Nicola Spurrier says there has been heavy travel across the border during the almost three-week exposure period.
"It's quite possible that we do have COVID in our community because of that traffic back and forth across the state," Professor Spurrier told reporters on Monday.
"The amount of testing done here in our state really is not high enough for me to feel absolutely confident about whether we may or may not have something happening here.
"So this is not the time to be complacent. This is the time to be really vigilant about all of the things we know can get us in front of this deadly disease."
Prof Spurrier said while there had been long queues at testing sites last week, the numbers had since dropped off significantly.
"I was a little bit disappointed over the weekend when I saw the number of testing being done in South Australia was about 4000 or so," she said.
"In Victoria they're having 40,000, 50,000 people being tested every day."
Premier Steven Marshall urged South Australians to get tested and vaccinated when eligible.
"Obviously there is a risk associated with this current outbreak in Victoria," he said.
"Our plea to the people of South Australia at the moment is don't take any risks ... if you develop any symptoms whatsoever, go and get yourself tested."