The pension arm of Australia's biggest bank has been hit with at least three such lawsuits, highlighting the intense scrutiny the sector faces after a government-backed inquiry showed systemic over-charging of fees.

The law firm, Shine Lawyers, had said in a statement earlier this week that Colonial First State encouraged customers to pick policies by CBA's insurance unit CommInsure, leaving them with higher premiums.

"These customers were forced to pay more for life insurance as well as total and permanent disability insurance, and this has eaten into their superannuation," its class actions practice leader Rebecca Jancauskas had said.

The country's biggest bank said it was reviewing the claim, while the law firm said it acted on behalf of "hundreds of thousands of Australians".

(Reporting by Nikhil Kurian Nainan in Bengaluru; Editing by Arun Koyyur)