Optus has admitted to the SA government calls were out of action for 10 hours on Thursday and SA police worked through Friday night conducting welfare checks on 150 people whose triple-zero calls failed, SA Premier Peter Malinauskas said on Saturday.
SA police said an eight-week-old boy from Gawler, on Adelaide's northern fringe, and a 68-year-old woman from the Adelaide suburb of Queenstown died during the outage.
The third death linked to the incident, which involved up to 600 attempted triple-zero calls, occurred in Western Australia.
It was not yet known if the failed triple-zero calls had a "material impact" on the emergencies in which people had died.
Optus had a duty to inform authorities as quickly as possible "and the fact that didn't occur until after a press conference on Friday beggars belief", Mr Malinauskas said.
"They've got to make sure they're letting our emergency services know ... all the information the moment they have it, before they think about crafting a media statement," he said.
"It is somewhat extraordinary we had a situation (on Friday) after everything that had unfolded, that we were still struggling to get information from Optus to allow police to do their work."
Three customers, two in SA and one in WA, died after they were unable to call emergency services, Optus chief executive Stephen Rue confirmed on Friday.
Optus would be "held to account" and would need to explain why it initially said it was a two-hour outage before admitting it lasted for 10 hours, the premier said.
"Latest advice" indicated the outage was from shortly after midnight on Thursday and lasted until lunchtime on Thursday.
SA Police Commissioner Grant Stevens told the premier on Friday night Optus had only supplied the suburbs where the deaths had occurred.
"I then called the CEO of Optus and thankfully, it was rectified following that," he said.
"But the lack of information flow from Optus to the South Australian government's appropriate authorities is somewhat bewildering and it raises a lot of questions."
A thorough, independent examination was needed and "the state government stands ready to do that but we'll also wait and see what actions the commonwealth government wants to take about that investigation", he said.
Federal Communications Minister Anika Wells said the incident was "incredibly serious and completely unacceptable".
"The impact of this failure has had tragic consequences and my personal thoughts are with those who have lost a loved one," she said in a statement.
All telecommunications providers were obligated to ensure they carried emergency service calls and the outage would be thoroughly investigated, Ms Wells said.
Optus was continuing its "welfare checks" to ascertain any further customer impact, Mr Rue said.
The network technical problem has since been resolved and an internal investigation has been launched.
"I offer my most sincere and heartfelt condolences to the families and friends of the people who passed away," Mr Rue told reporters on Friday evening.
"I am so sorry for your loss.
"What has happened is completely unacceptable. We have let you down."
WA police said they were conducting welfare checks.
The federal opposition's communications spokeswoman Melissa McIntosh expressed deep concern the triple-zero camp-on arrangements to divert calls to other carriers had also failed.
The incident occurred almost two years after more than 10 million Optus customers and businesses were disconnected for more than 16 hours in November 2023.
People could not call triple zero on landlines, although it was still possible to do so on a mobile.
The telco was fined more than $12 million for breaching emergency call rules during the nationwide outage.
Mr Rue took over as the company's chief executive in 2024 from Kelly Bayer Rosmarin, who resigned over the 2023 outage.
