South Australia will send the “strongest message possible” to people breaching the state’s COVID-19 border restrictions, with jail time under consideration, Premier Steven Marshall says.

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 just after 5pm 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 was convicted and fined $3000 and Thomas Forster, 35, was convicted and fined $3600.

The third person was still to appear.

South Australian Premier Steven Marshall is considering jail time for illegal border jumpers. Photo: AAP

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

But he said 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.”

Commissioner 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,” Commissioner 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 to 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.