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Police are treating the deaths of a woman and her toddler as a murder-suicide.

The tragic update comes as the search for a three-month-old along the cliffs of Port MacDonnell, off South Australia’s Limestone Coast, enters its third day.

Emergency services were first contacted after a car was found abandoned near Cape Northumberland about 11.15am on Monday with its engine running.

Soon after, officers located the bodies of a 36-year-old woman and a toddler in the ocean, who have since been identified.

The woman, Helena Wright, was from Compton, near Mount Gambier, and her daughter was 23 months old.

Ms Wright was originally from Estonia.

The search for her missing baby son is ongoing across land, sea, and air by police, the SES, and community volunteers.

On Wednesday, police said there was no indication anyone other than the mother and her two children were involved in what they called a “heartbreaking incident”, and it is being investigated as a murder-suicide.

“We are extremely grateful to the dedicated SES members, volunteers and SAPOL personnel who have worked tirelessly throughout the investigation and search operation,” a spokesperson said.

“Their professionalism, commitment and compassion during these difficult circumstances have been invaluable.”

They said a decision would be made later on Wednesday about the continuation of the search, based on the likelihood of locating the infant.

Ms Wright’s husband — the father of the two children — has been interviewed by police.

Superintendent Trent Cox said hope had been lost of finding the baby alive.

“Sadly, it’s a retrieval effort,” he said.

“We will continue to search this afternoon and then make decisions about whether we continue or discontinue based on the expert advice.”

Supt Cox said extremely challenging conditions had hampered the search, forcing emergency vessels to stay out of the water for much of Tuesday and limiting efforts to shoreline and clifftop sweeps.

“We’ve been unable to … to launch water assets. We’ve been able to get the SES aerial drone up,” he said, adding that experts had advised against deploying an underwater drone in the dangerous conditions.

SA Premier Peter Malinauskas said the tragedy had shocked the community to the core.

“If it involves children, that breaks your heart … particularly when we know there was a two-month-old baby missing. That’s hard to get your head around,” he said on Tuesday.

Police are calling on anyone who may have seen the car, a white 2015 Isuzu MUX with SA Registration S592BJR, or has any dashcam footage to contact Crime Stoppers on 1800 333 000 and quote #195585.

A report will be prepared for the coroner.

Lifeline: 13 11 14

beyondblue 1300 22 4636