The communications regulator is investigating Telstra's widespread network disruption on Wednesday that hit transport, businesses, emergency services and healthcare.
The issue was largely resolved by mid-morning and a solution for a separate "secondary issue" that prevented some users making triple-zero calls was in place by Thursday afternoon.
Telstra advised customers to immediately retry emergency calls if they did not go through, with 639 welfare checks carried out.
A software issue affecting nodes responsible for keeping time across Telstra's mobile network has been blamed for the outage.
The overwhelming majority of welfare checks had taken place with no adverse outcomes reported, Communications Minister Anika Wells said on Thursday night.
"The government is waiting on reports from an outstanding 13 welfare checks from states and territories," she said.
But South Australian Liberal Senator Kerrynne Liddle said her office received a report an elderly South Australian woman had died during Wednesday's outage.
South Australia Police said it had repeatedly attempted to contact Senator Liddle for information regarding the report without success.
The force later confirmed an individual died at a regional hospital on Wednesday but police had not been notified of the death.
An investigation into the cause and circumstances has begun.
Telstra chief financial officer Michael Ackland described the company's back-to-back technical mishaps as "an unfortunate incident" that was unacceptable to customers.
"Mobile networks are complex and we will continue to work through further changes to ensure we have the most robust solution but customers can feel confident in calling triple zero,'' he told reporters.
The company said overnight work had reduced the separate triple-zero error by about 90 per cent as engineers continued to eliminate the bug.
Mr Ackland said the company had completed 639 welfare checks since Wednesday morning.
Customer reports suggest problems began about 3am and Telstra said it became aware by about 4.30am.
Of those, 402 cases required followed-up voice calls, with 170 calls passed to police.
Mr Ackland defended the time Telstra took to contact the communications minister, whose office was told of the first outage about 7am on Wednesday.
Ms Wells has since demanded "total transparency" from the telco, saying it should have acted as soon it became aware of something the public needed to know.
"What Telstra knew, when they knew it and how they communicated it to stakeholders will be the subject of investigation," she said on Thursday.
"Telstra needs to account for how and why that has occurred because Australians are right to expect that as a baseline service from their telco."
There were still gaps in the emergency communications system that needed to be plugged immediately, Telecommunications Industry Ombudsman Cynthia Gebert said.
"It's fair to say the Telstra outage yesterday shines a further light on the whole triple-zero ecosystem to work much more effectively for end users than it did," she told ABC News on Thursday.
The Australian Communications and Media Authority has begun preliminary investigations into the outage.
Transport operators continue to deal with the fallout from Wednesday's outage.
All regional V/Line train services across Victoria were suspended as signalling systems were tested, with delays and cancellations continuing into Thursday evening.
In 2025, Ms Wells increased penalties for telcos that fall foul of their triple-zero obligations to $30 million.
Asked whether individuals within Telstra should be punished, Ms Wells said her focus was getting services back online.
"And then investigation can take foot, and we can learn out of that, and penalties can be administered, justice can be served," she said.
It is the third major national outage in less than a year for the $56 billion giant, which powers about 25 million Australian mobile services.
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