South Australians are being advised to reconsider any travel to Victoria in response to the COVID-19 cluster in Melbourne.
Chief public health officer Nicola Spurrier says extensive contact tracing has been done by Victorian authorities, but she encouraged people intending to travel in the next few days to be flexible with their arrangements.
She said it wasn't necessary to close the border at the moment.
"I am very hopeful the situation in Victoria will come to an end," she said on Sunday.
People in South Australia are also asked to follow instructions on Victoria's Department of Health and Human Services website if they have been in exposure sites which are being regularly updated.
"At the moment I would be saying to South Australians remain alert, but not alarmed," Professor Spurrier said.
Two close contacts of the Victorian cases are in quarantine in South Australia, but have tested negative.
South Australia recorded no new cases, but a returned traveller has tested positive to highly infectious UK-variant of the coronavirus.
Authorities encouraged people to get tested if they had any symptoms and to be alert if they have travelled to Victoria or been with friends and family who visited the state from Victoria.
Earlier anyone who had been to the coronavirus exposure sites identified by Victoria authorities was told to isolate for 14 days and get tested on day one, five and 12.
The tighter security followed a decision by authorities on Thursday to impose a hard border with NSW, preventing anyone from that state entering SA, in response to the virus clusters in Sydney.
Only returning residents, people permanently relocating and essential travellers are exempt from the new rules.
Returning residents or people relocating will still need to quarantine for 14 days and can only make that trip once.
A 100-kilometre buffer zone on the SA-NSW border allows cross-border residents free movement across the state line.
People in Australia must stay at least 1.5 metres away from others. Check your jurisdiction's restrictions on gathering limits. If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080. News and information is available in 63 languages at .
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