By Renju Jose

SYDNEY (Reuters) -Australia said on Thursday it would investigate an outage at telco Optus that cut off internet and phone connections to nearly half of its population, causing widespread chaos and leading some small business customers to seek compensation.

More than 10 million Australians were hit by the 12-hour network blackout at the nation's second largest telco for much of Wednesday, triggering fury and frustration among customers and raising wider concerns about the telecommunications infrastructure.

Optus apologised again on Thursday and blamed the outage on a "network event" that triggered a "cascading failure". It did not elaborate. Optus has previously ruled out a cyber attack.

Customers will be given free data "to acknowledge their patience and loyalty" CEO Kelly Bayer Rosmarin said in a statement.

Hours earlier, the government announced a post-incident review into the outage that hit payments, transport and hospitals and about 40% of the population. Communications Minister Michelle Rowland describing the incident as "particularly concerning".

"While we welcome that Optus services were restored over the course of the day, it is critical the government conducts a process to identify lessons to be learned from yesterday's outage," Rowland said in a statement.

Australia's media regulator will conduct a separate review into the outage after emergency triple zero ("000") calls went down on Optus landlines, Rowland added.

Taxi driver Ian Martin-Brown told Nine Network that he might take legal action after losing a day's work. Other customers including cafe owners and niche online retailers told media outlets they would seek compensation for lost revenue.

"There's no doubt that it has to be on the table," Assistant Treasurer Stephen Jones told ABC Radio. "If you're a small business that's lost a day's takings because your phone system wasn't working then you're going to be asking those hard questions."

Parent company Singtel said the outage had "let down our customers" and apologised as it reported on Thursday an 83% jump in half-yearly profit.

But UBS analysts said Optus now faces the possibility of losing customers to Telstra, the nation's largest telco firm, and TPG Telecom due to "strong brand perceptions" of the network quality of rivals.

The government said it would also check the possibility of allowing customers to switch to available networks when future outages occur.

"The industry is prepared to be involved ... it is feasible and we're going to take this forward as a government," Rowland told the ABC.

(Reporting by Renju Jose in Sydney; Editing by Jamie Freed and Miral Fahmy)