A botched firewall update at 12.30am on Thursday blocked hundreds of calls to triple zero in South Australia, Western Australia and the Northern Territory.
An eight-week-old boy and a 68-year-old woman died in Adelaide during the fault, along with a 74-year-old man and 49-year-old in Perth.
Optus was unaware of the outage for triple zero calls until being notified by a customer about 1.30pm, Optus chief executive Stephen Rue said.
The update was cancelled and access to the emergency line was restored after 13 hours.
Mr Rue admitted Optus had been contacted by the telecommunications industry ombudsman about two complaints of people trying to inform the company about the outage.
"Early review suggests that we had not handled these calls as would be expected," he told reporters in Sydney.
"Optus will be appointing an independent person to lead a review into this entire incident from every aspect, I hope to confirm that person in coming days."
Mr Rue pledged to give daily updates as more information about the grave incident came to light and said Optus accepted full responsibility for the problem.
Nationals leader David Littleproud said the behaviour of Optus, as a universal service provider, was "abhorrent".
"The fact that Optus has just in some blasé way ignored the risks that are there for Australians to be able to ring triple zero is just beyond belief," he told Nine's Today on Sunday morning.
"They do need to face penalties for this, the government needs to crack down."
The review must focus on the company's back-up plan for failed upgrades, or if it even had one, former Nationals leader Barnaby Joyce argued.
With Australia on the verge of bushfire season, the federal coalition is calling for a broader independent investigation into the triple zero network.
"There must be no delay in answers being provided and action taken to ensure Australians are safe," federal opposition communications spokeswoman Melissa McIntosh said.
SA Premier Peter Malinauskas suggested Optus did not pass on adequate information to the state's police after the outage, hampering locating people who needed help.
Mr Malinauskas said it took a call from him to the Optus CEO before the problem was fixed.
"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," he said.
Federal Communications Minister Anika Wells slammed the telco for failing to heed the recommendations of a review into a November 2023 outage when customers were also unable to contact triple-zero.
Mr Rue defended not publicly revealing the outage until Friday night in a snap press conference more than a day after the problem was identified and rectified.
He said Optus was focused on determining the facts and conducting welfare checks before informing governments and the public.
Ms Wells questioned how the incident could occur again after a review identified problems Optus should have addressed.
"We're disappointed that it's happened again, no triple-zero outage is acceptable and this will be thoroughly investigated," Ms Wells said.
"Many of the things that happened in this outage are failures to implement some of those recommendations, including alerting the public or emergency services authorities."
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