* CBA cuts top executives' bonuses to zero
* Says CEO Narev retains board's confidence
* Board cuts directors' fees by 20 pct (Adds quote and details)
MELBOURNE, Aug 8 (Reuters) - Commonwealth Bank of Australia CBA.AX on Tuesday scrapped its chief executive's bonus for damaging the bank's reputation amid allegations it broke money-laundering rules, but said he retains the board's confidence.
Australia's biggest lender has been accused of 53,700 breaches of anti-money laundering rules, including failing to identify, monitor and report transfers of more than A$10,000, which could result in several billion dollars of fines.
CBA has blamed the breaches largely on a software error. board said on Tuesday it has cut short-term bonuses to zero for Chief Executive Ian Narev and other top executives for the year to June 30, 2017.
"In reaching this conclusion the overriding consideration of the Board was the collective accountability of senior management for the overall reputation of the Group," Chairman Catherine Livingstone said in a statement.
"Mr Narev retains the full confidence of the Board," she said.
Sharing some accountability, Livingstone said directors' fees have been cut by 20 percent for the 2018 financial year.