South Australian police have arrested two teenage boys for the alleged murder of a woman at Callington, south-east of Adelaide.

Pirjo Kemppainen, 63, was found dead in her house on Saturday afternoon by her brother.

The first boy was arrested at his Callington home about 4:00pm on Tuesday while the second boy, also believed to be from Callington, was arrested about 6:30pm.

Acting Superintendent Denise Gray, who is heading the investigation, would not say whether the boys were the same teenagers who visited the woman's home the day before she died.

The boys are due to face the Youth Court.

The Finnish migrant and former nurse had called police 16 hours before her body was found to report that her glass door had been smashed.

But police say they did not send a patrol to her home due to a call centre operator failing to pass on the information.

It is an error that has shaken public confidence and provided an unwelcome distraction for the investigators.

Superintendent Gray says she wants the focus to be on the murder case.

"People need to trust the police and come forward to the police," she said.

"And it's very important we get community cooperation and that we don't lose focus."

The police assistance line is for not for emergencies. Hours before her death, Ms Kemppainen had told the call centre a rock had been thrown through her glass sliding door.

Neighbours said she had been fearful.

An internal inquiry has begun into why the police call centre did not pass on the woman's concerns in the hours before her death.

Police Commissioner Mal Hyde has been defending the system on ABC Radio, saying the public servant who took the call got it wrong.

"I've been quite up-front about this. There's no covering up of anything, but what I'm saying is that a poor decision was made on this occasion," he said.

"We're not saying that's acceptable. We're saying that's not acceptable. And we're looking into it to see whether or not, in terms of our procedures or training or whatever it is, we can improve upon to make sure it doesn't happen in the future."

But Mr Hyde's explanation has infuriated the Public Service Association (PSA).

Union official Peter Christopher says the operator was not obliged to send out a patrol.

"I believe this person has been hung out to dry and the PSA is quite appalled by how the matter has been dealt with," he said.

The South Australian Opposition called for an independent inquiry into the matter.