Police Commissioner Grant Stevens has also backed the option of prison sentences for border breaches after the arrest of three people from Victoria.

The trio crossed the border on Saturday, with one of them claiming to need urgent medical attention, although they later failed to attend a nominated hospital.

Their ute was found at suburban Mawson Lakes just after midday on Sunday.

In Adelaide Magistrates Court on Monday, Elissa Griffiths, 32, was fined $3000 while Thomas Forster, 35, and Matthew Griffiths, 36, were each fined $3600.

All three pleaded guilty to failing to comply with a direction.

Mr Marshall says the most important thing is to have the trio returned to Victoria as soon and as safely as possible.

But he says the government would look at adding jail time to the penalties courts could impose.

"This is something we're happy to consider," the premier said.

"We want to send the strongest message possible to anybody that comes into our state that if they're doing the wrong thing, there are significant penalties.

"We can't be too casual in regards to the coronavirus.

"There are devastating results now being felt from a health perspective and also from an economic perspective in Victoria."

Mr Stevens said while fines, including on-the-spot penalties and those imposed by the courts, could act as a significant deterrent, he would also back making a prison term an option.

"I'd certainly support it. It's an opportunity to add some weight," Mr Stevens told ABC radio.

But the commissioner conceded that some people would still try to breach border restrictions regardless of the consequences.

"That's why we've got so many police, supported by the defence force, on our borders trying to keep an eye on everybody coming across," he said.

Under current rules, anyone breaching COVID-19 regulations in SA is liable for a $1000 on-the-spot fine, but could also be taken to court where the maximum penalty is a $20,000 fine.

But four men who stowed away on a train from Melbourne last week caused controversy when they were placed on good behaviour bonds without any immediate monetary penalties.

SA reported no new coronavirus cases on Monday, leaving the state's total since the start of the pandemic at 444.

There are no active infections.

Australian Associated Press