Telstra says it has restored most online services including Bigpond email access for the majority of customers affected by a potential security breach.

"Most online services including BigPond email and My Account are back online, load times may be a touch slower than usual," Testra said on Twitter.

The services were suspended after account information, including passwords, was published on the internet, but Telstra says bank and credit card details were not disclosed.

Telstra says around 60,000 people have been affected by the outage.

The Australian Communications Consumer Action Network (ACCAN) says the privacy breach was a major bungle by Telstra.

The network's spokeswoman Elise Davidson says a Telstra database with up to 1 million customers' personal details including passwords was left open for anyone to view.

"We wanted to test it and we did and sure enough it was readily available - things like passwords, the details of problems having or wanting to change bundles," she said.

"Basically any contact that you would have with the customer centre about your bundle was readily available for anyone to see."

Ms Davidson says it is "almost unbelievable" that Telstra could let the bungle occur.

"ACCAN have been speaking to Telstra. They are obviously taking it very very seriously and are investigating," she said.

"It is hard to imagine how an error of this magnitude has happened, has been allowed to happen for a company the size of Telstra, with the number of the customers they have."

Ms Davidson says Telstra may be liable for compensation in some cases.

"Some people for example might wish to have credit or security checks done on their information," she said.

"There's a fee for that - maybe Telstra's going to cover that fee, maybe they're going to be required to give some sort of compensation in some other way, we really don't know the extent of it."

Telstra said technicians are currently working on the problems and it expected to restore services around mid-afternoon; however a spokesman said at 3.30pm AEDT that "at the worst it shouldn't be longer then 24 hours from now".

The company is updating customers on the situation at its Twitter feed @Telstra.