A failed emergency call during a widespread Optus outage is unlikely to have cost a baby boy his life, police say.

A botched firewall update on Thursday blocked hundreds of calls to triple zero in South Australia, Western Australia and the Northern Territory.

An eight-week-old boy from Gawler West, north of Adelaide, was among four deaths authorities had linked to the fault.

While the boy's family was impacted, police now believed the outage is "unlikely to have contributed to the death".

"The deceased boy's grandmother has told investigating police that she attempted to call 000 using her mobile phone when she was alerted to the fact her grandson was not breathing," SA Police said in a statement on Sunday.

"When her call was not connected, she immediately used another mobile telephon

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