Speaking at a press conference about CBA's 2015 half-year result, Mr Narev pointed to the December 2014 finding of the OAR independent expert, Promontory Financial Group, that the program is "fit for purpose".
With those "foundations" in place, the main focus for the bank has been to make sure "everybody who may have received poor advice from 2003 to 2012 knows about the program", he said.
The OAR, which is open for registration until July 2015, has had just over 1,200 registrations, Mr Narev said.
"We’re also very focused on making sure that the assessments occur and people can see the outcome of the Open Advice Review program," he said.
To that end, the first assessments of the OAR are now "in the hands" of affected customers through the "independent advocates" (ie. Shine Lawyers, Maurice Blackburn Lawyers and Slater & Gordon) who are representing them, Mr Narev said.
"That will now continue and gain momentum, focusing first on customers with particular hardship.
"Since the program is open for registration until July we expect to keep working hard on these assessments through this year and probably through most of next year as well," Mr Narev said.
The bank has paid out $50 million to customers who have received poor advice "over a large number of years", he said.
CBA's half-year result revealed another hefty profit for the bank, with statutory net profit after tax up eight per cent to $4.54 billion.
The wealth management business was up one per cent with "really strong performances in the funds management business", Mr Narev said.
"Flows into the platform have been very good. Funds income is up seven per cent," he said.
"Average funds under administration [is] up 11 per cent and the funds themselves performing really well," Mr Narev said.
CBA also announced a fully franked interim dividend of $1.98, up eight per cent on the 2014 interim dividend.