SYDNEY (Reuters) - Commonwealth Bank of Australia sold credit card insurance to about 64,000 customers who were not eligible to claim against it, including students and pensioners, an inquiry into Australia's financial sector heard on Monday.

The evidence of widespread mis-selling also extended to loan protection products for personal and home loans, CBA said, heaping pressure on the country's biggest lender which is also under fire over an apparent reluctance to compensate customers.

Internal documents referred to at the inquiry on Monday showed that CBA's CreditCard Plus product was sold to tens of thousands of customers who were not employed, although employment was a pre-requisite to qualify for cover.

"There were many customers who did not meet the criteria to whom we sold it," CBA Executive General Manager of Retail Products Clive van Horen said, under questioning.

CBA failed to take "reasonable steps" to ensure customers were aware of the product limitations when it was sold with CBA-branded credit cards between 2011 and 2015, he said.

The mis-selling was magnified by the bank rewarding sales staff with bonuses and prizes for beating targets, the inquiry heard.

CBA acknowledged in an email to staff late last week the inquiry would hear of instances "where customers have been treated unfairly".

The year-long inquiry, called a Royal Commission, can recommend criminal or civil prosecutions and legislative changes, potentially forcing changes to bank practices.

The centre-right government reluctantly agreed to call the inquiry in response to a series of banking scandals including interest-rate rigging and breaches of anti-money laundering laws by CBA.

Under regulatory pressure to boost their cash reserves, Australia's big retail banks, which include CBA, Australia and New Zealand Banking Group, National Australia Bank Ltd and Westpac Banking Corp, have been ridding themselves of cost-intensive and at times problematic insurance and non-core assets recently.

CBA was also questioned on how it was compensating affected customers, which included a "call to action" letter asking them to make a claim on problematic insurance products.

Van Horen said that the response rate for such letters was around 30 percent, prompting the inquiry to question how hard the bank was trying.

"I can say with conviction ... we had no intention to sweep the matter aside or pretend it didn't exist," Van Horen said.

BROKER RELATIONSHIPS

Bank and broker relationships have been an early focus of the inquiry, with ANZ accused earlier on Monday of failing to assess whether customers referred through brokers could service their home loans before approval.

Home loans are big drivers of growth at Australia's highly profitable "Big Four" banks, which dominate the country’s tightly held A$1.7 trillion ($1.3 trillion) mortgage market. About half of all mortgages are written by brokers, according to the inquiry.

Barrister assisting the inquiry, Rowena Orr, said there was no system at ANZ of "verifying customers' expenses" as stated to mortgage brokers, other than their existing liabilities to the bank.

ANZ’s general manager of home loans and retail lending, William Ranken, agreed with Orr but said brokers risked losing their accreditation to recommend ANZ loans if they failed to properly assess applications.

($1 = 1.2989 Australian dollars)

(Reporting by Jonathan Barrett in SYDNEY. Additional reporting by Paulina Duran; Editing by Stephen Coates)

By Jonathan Barrett