Telstra has announced it will be providing a $25 credit to thousands of its internet customers who were offline for an extended period of time due to its most recent network outage.

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On Friday, Telstra executives finally spoke out about the mass ADSL and NBN internet outage that began on May 19 with Telstra's chief operations officer Kate McKenzie publicly apologising to affected customers.

"We'll be contacting customers directly who were offline for an extended period to apologise and offer them a credit," Telstra tweeted this morning in response to a customer query about the $25 credit that would be automatically provided to their account.

The company acknowledged on Friday that the outage had, at one stage, affected 10 per cent of their internet customers — roughly 370,000 people.

But Telstra could not confirm the exact number of those eligible for compensation, with Telstra's James Kelly saying it would be in the "single digit thousands".

This is despite Ms McKenzie confirming on Friday that roughly 15,000 people were still unable to connect to the network last week.

"Customers can have conversations with us if they want other forms of compensation," Mr Kelly told the ABC.

Mr Kelly also confirmed the company was having "separate conversations with businesses about compensation and what their needs are".

Some took to social media following Telstra's email, with one user speculating the company "may have learnt" from their previous free data days.

"[In] April they gave a Sunday of unlimited data. I smashed it with music and audible books. They may have learnt from that," they tweeted.

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Telstra was widely criticised this week for twice publicly announcing online everything was fixed when some customers were still affected.

The company announced in early May it would spend an additional $50 million on its mobile network in a bid to prevent ongoing outages.

The first big outage in February was caused by what Telstra at the time called an "embarrassing human error".

There were more problems in March after a failed international cable affected domestic operations, again bringing down the national mobile network.

Experts have said the way the company has handled this latest major outage — the fourth of 2016 — has seriously damaged the brand.