Speaking for the first time since a Senate committee last week called for a royal commission into the scandal, Mr Narev said their behaviour was unacceptable.
"We know this is unacceptable and I unreservedly apologise to all customers affected," he said in a statement on Thursday.
"Poor advice provided by some of our advisers between 2003 to 2012 caused financial loss and distress and I am truly sorry for that."
Mr Narev said the bank was setting up an open advice review program in an attempt to prevent a repeat of the scandal. He said the program would be operational from mid-August.
The program will allow any customer who received bad advice from the financial planners at the heart of the scandal between 2003 and 2012 to have their cases reviewed.
It will also oversee an in-house review by the bank into the advice its financial planners gave to customers during that period.
Commonwealth Bank has so far paid out $52 million in compensation to affected customers.
He said that more cases could come to light during the review program.
"Because we are being so open, it is very possible that we are going to learn about new instances that we didn't know about."
Federal opposition leader Bill Shorten says the bank is now embroiled in a "scandal of shocking proportions" and should not put the onus on affected customers to step forward.
"The onus should not be on consumers to have to come forward and take the efforts to identify their own losses," Mr Shorten told reporters in Melbourne on Thursday.
"The bank should be working with consumers, with people it has provided advice, to ensure these people know their rights.
"This is a scandal of shocking proportions - thousands of people have lost their money for no other reason than they trusted the advice and the institution that provided the advice."
Mr Shorten said the government should consider a royal commission into the bank's conduct, and not proceed with its planned reform of financial advice laws which Labor says will further water down consumer protections.
"To the Abbott government, how many victims of financial advice do you need before you will stand up for the victims and consumers against the vested interests?" Mr Shorten said.
"We don't think that the matter should rest here but whether or not a royal commission is the right vehicle remains to be seen."
