"We're deeply sorry that a cyberattack has happened on our watch," the company said in the notice.
"We know this is devastating and that we'll need to work hard to regain your trust," it said.
The new page on the company's web site offered support to customers whose data has been breached, including how to replace drivers' licenses, passport and health care card numbers.
The company has agreed to pay the cost of replacing passports of compromised customers, Prime Minister Anthony Albanese said on Friday.
"We will be in touch with customers who have had their passport document number exposed," Optus said on its web site.
Australian police said on Friday they had set up an operation to beef up protection of more than 10,000 Optus customers whose identity credentials had been shared online due to the data breach.
Authorities have declined to comment on their investigation and effort to find the hacker since the telcoms giant on Sept. 22 first reported the theft of the data of up to 10 million accounts, equivalent to 40% of Australia's population.
(Reporting by Sonali Paul)