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The network dropped out about 4am yesterday, with people unable to connect to the internet or make or receive calls.
Engineers have spent hours trying to uncover the source of the outage and bring the system back online, Optus chief executive Kelly Bayer Rosmarin said.
"The team has tried a number of paths of restoration," she told ABC Radio Sydney on Wednesday.
"So far, we have not had the result we have hoped for and we're pursuing every avenue to get everybody back online as soon as possible."
Ms Bayer Rosmarin confirmed people could not make calls to triple zero on Optus landline devices although it was still possible to do so on a mobile phone.
Close to 10 million Optus customers had their personal information stolen when the company's data system was breached last year.
There was no indication Wednesday's outage was the result of a cyber attack, Ms Bayer Rosmarin said.
"This is a very, very rare occurrence and when I have more information about the root cause, I will be the first to let all our customers know," she said.
Federal Communications Minister Michelle Rowland said Optus needed to be transparent with its customers, who were experiencing "a high level of anxiety and frustration".
"Consumers will be making judgments about the quality of service that they receive in a competitive market," she told reporters.
"It is important at this time that people have their services restored as soon as possible."
Ms Rowland encouraged consumers, especially small businesses, to keep receipts in case they choose to pursue any compensation.
The Telecommunications Industry Ombudsman also advised affected customers to lodge a complaint if they have contacted Optus and are unhappy with the response.
"We can help you with refunds for the time you have been unable to use your service, compensation claims and disputes about your contract," the statement read.
Melbourne train services were also interrupted early on Wednesday, reportedly due to the Optus outage.
All metropolitan services were stopped from about 4.30am due to a communications fault across the train network.
Metro Train services started to resume just before 6am but major delays continued throughout the morning peak as services were restored.
"We apologise to our passengers for the delay to their travel this morning," Metro Trains chief executive Raymond O'Flaherty told AAP in a statement.
"We thank passengers for their patience while trains return to their normal timetable."
Service NSW call centres, Victoria's virtual emergency department and Northern Health hospital phone lines were also down due to the Optus outage.