The interim chief executive of embattled stockbroker Davy has written to clients to offer an "unreserved and unequivocal" apology for the events that led to a recent fine of €4.1m from the Central Bank.

Bernard Byrne said he fully acknowledges that Davy had failed to adhere to the standards that are expected of it.

"You undoubtedly have questions arising from the matter," he wrote.

"This letter is intended to answer some of the questions you may have surrounding the investigation itself and the actions we have taken since the findings of the investigation were announced."

The message includes a link to a questions and answers page where the firm outlines the steps it is putting in place to address the failures around the controversial 2014 bond transaction.

The Central Bank found that Davy had breached a number of market regulations in relation to the deal, which involved a client selling Anglo Irish Bonds to a buyer without being told the purchaser was actually a consortium of 16 Davy figures.

"I would like to stress that the information provided is in no way an attempt to justify or minimise the seriousness of the findings which have been made against Davy but are presented in order to provide assurance around the robust position of the firm and the many strong controls that do exist," Mr Byrne wrote.

"The failures at Davy have impacted our reputation and your trust in us. As the new leader of Davy I will do everything I can to rebuild that trust. We remain fully committed to and focussed on serving your needs."

On this day last week, the chief executive of Davy, along with the deputy chairman and head of bonds all resigned because of the affair.

Last Monday, the National Treasury Management Agency withdrew Davy's authority to act as a primary dealer of Irish Government bonds.

Davy then closed its bond desk, making four staff redundant, and said none of those involved in the consortium were working for the firm any longer.

On Thursday evening, Davy’s board said it had decided to pursue a sale of the firm.

Meanwhile, it is understood that Davy is close to appointing an independent third party firm to carry out an internal review of the Central Bank findings.