Telstra chief executive Andy Penn has pledged to provide another free day of mobile downloads to apologise for a national outage that affected more than eight million customers.

Speaking at the company's headquarters in Melbourne on Friday morning, Mr Penn apologised and blamed a system error for the outage. 

"At about 6pm last night a lot of our customers were disconnected due to an issue," he said. "It was the attempt to reconnect customers at the same time that caused the congestion."

Mr Penn said he was bringing international experts to Australia to conduct a deep review of Telstra's network and services.

He added that all mobile customers on Sunday, April 3 would get unlimited free mobile downloads as compensation.

"I'm sincerely sorry to all of our customers," he said. "At a personal level I'm deeply disappointed and I want to apologise to all of my customers.

"It affected around 50 per cent of the calls and we have about [16.7 million] customers on our network so can roughly approximate around 8 million customers across that time."

Users were unable to make calls or access the internet from their phones for around 4 hours during the evening commute period on Thursday night.

Mr Penn said the domestic mobile services were caused by a problem in Telstra's international undersea cable.

This was the second outage of Telstra post-paid mobile services in two months on top of one that affected pre-paid customers.

It will likely hurt Telstra's reputation as Australia's premium mobile network, which has allowed the company to charge its customers higher prices compared to rivals like Singtel-Optus and Vodafone Hutchison Australia.

Telstra's senior executives had pledged after the last national outage that it would be the last blackout to hit the network - a promise that was broken on Thursday night.

In February, the phone and internet giant blamed human error after an engineer caused a nationwide outage affecting millions of customers for several hours by accidentally switching off a core node.

Earlier this month about 500,000 Telstra pre-paid mobile customers also suffered network problems.

"One outage is not good enough ... and two is absolutely not acceptable and all I can do is apologise and say I'm committed to address this and do everything we can to ensure it doesn't recur," he said. "Obviously customers are disappointed as you can understand."