(CNN) Police in Australia say they've identified an alleged serial killer behind three previously unlinked murders but they can't arrest the suspect due to lack of evidence.

South Australia police made the extraordinary admission in a public call for help for information that could lead to the arrest of the suspect, a 39-year-old man in Riverland in the neighboring state of Victoria.

"We clearly know where he is. He knows he has been a focus of the investigation for many years, he knows that we're looking at it again now," Detective Superintendent Des Bray, the officer in charge of the Major Crime Investigation Branch, told reporters on Tuesday.

Police said new forensic evidence and other information had confirmed previous suspicions that a single suspect was responsible for three murders stretching back 20 years.

The cold cases include the deaths of Adelaide grandmothers Phyllis Harrison in 1998 and Beverley Hanley in 2010, and Stephen Newton, from Mount Gambier, in 2011.

Police revealed a secret task force, including seven detectives, had been reviewing the cases since January.

Suspect lived nearby

Police said the suspect was known to all the victims and at the time of their deaths had lived within about 10 minutes of them.

Bray said that police can't arrest the suspect because "[we want to] make sure we gather enough evidence so we can convict in court... to jump in early and arrest him without sufficient evidence and let him get off would simply expose the public to more risk."

The detective said that theft was the motive in all three murders.

"This was a cowardly attack on our grandmothers, on an elderly pensioner," he added. "Each attack was extremely brutal, and the type of people that commit these offenses are not worthy of people defending them. So I'd encourage anyone with information to think about it, consider their conscience, consider the families of each of the victims, and do the right thing now and come forward."

"It's clear that some people have withheld information and some people have told lies, and some of those people may be scared of this offender," he added.

Reward

A reward of $150,000 (A$200,000) is being offered for information that leads to a conviction in the cases of the two grandmothers. A separate reward is being offered in relation to the death of the third victim.

Harrison, 71, was found dead in her ransacked home in Elizabeth South, an Adelaide suburb. She had suffered multiple stab wounds, the online police statement said.

Bray said that she "was killed most likely because she knew her attacker and to stop her from identifying him."

The body of 64-year-old Hanley was found at her home in Elizabeth North, a neighboring suburb. She was doing her laundry when attacked and suffered severe head injuries, her house was ransacked and her handbag stolen.

"Importantly, a witness heard [Hanley]... talking to a male near the back door of the house, who she apparently knew," said Bray. "During the course of that conversation, their voices became elevated, and it was clear an argument developed, followed by a scream, some loud thuds, as someone had apparently been struck. Then silence fell."

The decomposing body of Newton, 55, was found in his home in Mount Gambier, said the statement. He died as a result of an assault, and his was body was discovered over a month later. A range of items including a TV, DVDs, a computer game console and games were taken.

"In this case it's possible that more than one offender may have been present at the time of his death, and in any event it's likely that more than one offender was involved in disposing the property that was stolen from his house," said Bray.

In Newton's case, a man was charged and convicted in relation to property theft and was sentenced to jail in 2012.

The families of the victims have previously released appeals about the cases, an ABC report said, and earlier this year Harrison's daughters spoke publicly about their mother's death.

"My son went in first and then I went in and I noticed that she was laying on the floor and I just freaked out," daughter Diane Smoker said, according to the report.

The family has previously indicated it believes Harrison's killer was someone she knew.

"They got into the house with her acknowledgment and that's when they took advantage of her," daughter Julie Lane was quoted as saying.