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.
Communications Minister Anika Wells has pledged to "hold Telstra's feet to the fire", saying the telco's response was not good enough.
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 officer 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. You have my commitment on that," she said.
As well as apologising to Australians for the outage, the Telstra CEO 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 not able to contact each other when their loved one became unwell.
"We extend our sincere apologies to the family for the role we have played in making a distressing day even worse for them," the spokesperson said.
The crisis has raised questions over the ASX-listed behemoth's actions.
In May, Telstra sacked more than 100 people and merged two of its largest technology divisions in a restructure.
Ms Brady denied job cuts had affected quality control systems.
Telstra's corporate leadership has also come under fire, with former federal treasurer Wayne Swan saying executive bonuses needed to be reconsidered.
Ms Brady deflected calls for her to slash executive bonuses.
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.
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.
Ms 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.
"It is beholden on all of us to address that gap. We've been working on it. We're closing it.
"It is not closed and we all need to do a lot more work to make sure that it closes."
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