In response to Fairfax Media reports which uncovered errors in the handling of claims, particularly relating to heart attacks, the CBA said it did not address the needs of some customers in a fair or sensitive way.
"It is clear that in relation to the customers who have been the subject of recent media enquiries, we failed to meet that responsibility," he said.
"In these cases we focused too much on process rather than people. By their nature, life insurance policies can be complex. Claims processes involve the review and assessment of detailed documentation. Whilst thoroughness is important for the integrity of the system, this must be balanced by customer need and dignity."
Mr Narev said he would write personally to clients who had had their claims mishandled and offer to meet them face to face.
"I am saddened and disappointed by the handling of these cases," he said.
However, Mr Narev emphasised that evidence showed that in a vast majority of cases, the right outcomes for customers were reached in the right way.
"In 2015, CommInsure paid more than $850 million of life and income protection payments to 22,000 people and their families," he said.
Mr Narev conceded the bank had "wronged" some of its clients at critical times and was moving to resolve the delays.
"As part of our relentless focus on values at Commonwealth Bank, people are encouraged to escalate concerns or difficult decisions. Here it appears that did not happen. These customers felt frustrated and let down by CommInsure, and believed they were more likely to have their voices heard by speaking to people outside Commonwealth Bank," he said.
"Having had these cases brought to the attention of senior management within the last few days, we have acted on unresolved matters."
Mr Narev urged customers to contact the bank directly to discuss their cases further.
Fairfax Media reported this morning that ASIC will investigate CBA's failing to pay claims since the definition of 'heart attack' the bank was using was "outdated".
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