Thursday's service interruption has been linked to several deaths and was the second time in two years that an Optus network issue meant Australians could not access the emergency line.
After the telco's 2023 outage, a review recommended the government implement a triple-zero custodian with oversight and responsibility for the emergency network, including monitoring its end-to-end performance.
Communications Minister Anika Wells conceded the role was yet to be fully implemented, although it had been set up.
Labor is yet to legislate powers for the custodian.
In accepting a recommendation in April 2024, the government said it recognised the need for a single body to oversee emergency call services and said it would have key co-ordination and decision-making authority during crisis events.
Opposition communications spokeswoman Melissa McIntosh noted the government had more than 18 months to implement the recommendations.
"It's beyond frustrating that it has taken another triple-zero network outage to find out those urgent recommendations have not been implemented in full, including the triple-zero custodian role," she told AAP.
"The Albanese Labor government has absolutely failed to ensure the triple-zero network is protected and that Australians can rely on calling help when it is needed most."
The custodian role will be performed by the communications department and the requisite legislative changes could be fast-tracked after the latest Optus calamity.
"That role has actually been established and is operative ... it's one of the recommendations of the Bean review that has been implemented but not yet in full," Ms Wells said.
"One of the things that I've been looking at across the weekend is how I can fast-track regulatory and legislative relief to make sure that all of these are delivered in full."
Parliament's lower house is next scheduled to sit in early October but the Senate won't return until later that month.
Opposition Leader Sussan Ley indicated the coalition would support legislation to empower the watchdog but said the bigger question remained around restoring trust.
"If legislation is required, we'll work with the government," she told Nine's Today program on Tuesday.
"But we do need to know the investigation is being done properly and it needs to be carried out by more than just the regulator."
Her comments echo those from Liberal frontbencher Tim Wilson, who wants a senate inquiry into the fiasco.
Thursday's outage, which Optus only revealed late on Friday, came 18 months after rival Telstra also failed to comply with emergency call rules during a triple-zero network disruption.
Optus copped more than $12 million in penalties after its first outage and could be subject to similar fines again.
An eight-week-old boy from Gawler West, north of Adelaide, was among the deaths linked to the fault.
But SA Police say the outage was "unlikely to have contributed" to his death because his grandmother immediately used another phone to contact triple zero.
The other deaths include a 68-year-old woman from Adelaide and men aged 74 and 49 from Perth.
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