Trust in the telecommunications company is in tatters after the network interruption hit transport, businesses, health and emergency services, leaving millions of customers in the lurch.
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.
The company has launched an internal probe and is under investigation by the federal government and the Australian Communications and Media Authority.
Executives are also set to front a snap meeting of a triple-zero parliamentary inquiry as early as next week.
Federal minister Jason Clare welcomed the scrutiny.
"People could have lost their lives and that's why there's an investigation by ACMA," he told reporters in Sydney on Saturday.
"They're liable to some very serious financial penalties for what's happened here."
Telstra has 45 days to report to the regulator and could face civil penalties under powers introduced by the government after the 2025 Optus outage.
A confirmed breach of emergency services obligations could lead to fines of up to $30 million.
Telstra says a critical software fault caused the outage that halted train lines and timed out business transactions.
The national disruption forced Telstra to conduct 639 welfare checks on triple-zero users, with seven requiring assistance after initially failing to get through.
Telstra chief executive Vicki Brady said she took responsibility to maintain trust in triple zero "extremely seriously".
"We will complete our investigation into the actions needed to prevent it from happening again," she said.
As well as apologising to Australians for the outage, Ms Brady had spoken to the family of an elderly woman in South Australia who died during the disruption, a spokesperson said.
Telstra and SA Police concluded the outage was not responsible for the woman's death but Ms Brady apologised and offered her condolences to family members who were unable to contact each other when their loved one became unwell.
The crisis has raised questions about the ASX-listed behemoth's actions.
In May, Telstra sacked more than 100 people and merged two of its largest technology divisions.
Ms Brady denied job cuts had affected quality control systems.
RMIT associate professor and telecommunications expert Mark Gregory said Australia's legislation needed to be rebuilt, "structurally from the ground up and in tune with the modern era".
"We need to start again," he told AAP.
"We've seen piecemeal changes being made to the telecommunications legislation and to the regulations.
"What we need to do is to rebuild the Telecommunications Act, the legislation and the regulations, and to make them fit for purpose."
The act, which came into effect in 1997, was written "back when the internet was brand new", Dr Gregory said.
"Smartphones were not invented, the big tech companies didn't exist ... streaming and all the other things we use these devices for didn't happen," he said.
"Connecting railway networks over mobile didn't happen."
The crisis comes less than a year after an Optus network failure - which went for almost 14 hours - left hundreds of people unable to call triple zero and was linked to two deaths.
Communications Minister Anika Wells acknowledged substantial improvements had since been made but conceded there was more work to be done.
"There is a large gap between the way that this industry has been regulated for a long time - 30 years - to what a modern customer expects of their telco," she said.
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