In what Premier Steven Marshall described as "completely and utterly unacceptable" the man failed to reveal he had worked at an Adelaide pizza bar, considered a hotspot for cases associated with the so-called Parafield cluster.

The outbreak grew to 25 confirmed infections on Friday, with 44 more suspected of having the virus.

However, the six-day statewide lockdown will now end at midnight on Saturday, three days early, with people allowed outside their homes to exercise immediately.

The man at the centre of the controversy initially told authorities he had only purchased a pizza from the shop when in fact he had worked several shifts at the location.

He contracted the disease from a fellow worker there, who was also a security guard at one of Adelaide's quarantine hotels, the initial source of the outbreak.

The revelation eased concerns about how the man, who also worked as a kitchenhand at another quarantine hotel, had become infected and who he had possibly spread the virus to.

"Their story didn't add up. We pursued them. We now know that they lied," Mr Marshall said.

"To say that I am fuming about the actions of this individual is an absolute understatement.

"The selfish actions of this individual have put our whole state in a very difficult situation."

Police Commissioner Grant Stevens said had the person been truthful to the contact tracing team, SA would not have gone into the six-day lockdown.

"The second consequence of that lie is this person has numerous associates that we are now trying to identify and locate," he said.

"There is an absolute need for us to move quickly over the next 24 to 36 hours to identify and locate these people.

"It's stating the obvious to say that this person's actions have had a devastating impact on our community.

"People's lives have been upended as a result of information that led us to a course of action that was now not warranted."

However, Mr Stevens said the Emergency Management Act did not give police powers to take any further action against the man.

Those provisions will be reviewed.

Chief Public Health Officer Nicola Spurrier said the Parafield cluster had grown by just three cases overnight.

The other 44 people suspected of having the virus are waiting on test results.

All the new and suspected cases are already in quarantine, with the total number of people in isolation rising to more than 4500.

Professor Spurrier said the number of confirmed infections was expected to rise over the next few days but urged people not to be alarmed by that.

She said efforts were continuing to put a "double ring-fence" around the outbreak to limit the risk of more widespread community transmission.

SA conducted a record 14,459 tests on Thursday, taking the total over the past three days to almost 36,000.

Professor Spurrier said she could not say why the person at the centre of the controversy lied.

"I'm not in that person's head. I don't understand why he said it," she told reporters.

"I am very disappointed that somebody wasn't able to give us the right information that we needed.

"(But) I don't know the person's circumstances. I don't know what pressures they were under."

The easing of the lockdown means from Sunday, SA will essentially revert to restrictions imposed earlier this week as the cluster first emerged.

That includes limiting numbers at gatherings such as weddings and funerals and at pubs, restaurants and other venues, and a general density requirement of only one person to each four square metres.

The stay-at-home requirements will be scrapped and masks, though encouraged, will not be mandatory.

Australian Associated Press