Telstra CEO Andy Penn is "deeply disappointed" following yet another nationwide interruption to the company's mobile services which occurred on Thursday, promising another "free data day" to make it up to customers.

The outage began about 6pm on Thursday and initially prevented 50 per cent of calls from going through, according to Mr Penn. He estimated 8 million customers — or half of Telstra's 16 million customer user base — were affected.

Most customers were back to full service within two hours, according to Mr Penn, although at 6.30am on Friday Telstra's official Twitter account was still replying to complaints, repeating the message it had been sending out for hours: "We're progressively restoring mobile services and anticipate returning to normal soon".