HSBC has issued a full-page apology in several newspapers over claims its Swiss private banking branch helped clients evade taxes.
In a letter addressed to customers and staff, chief executive Stuart Gulliver said the revelations over the past week had been a "painful experience".
The fallout from the revelations sparked a political row between the Conservatives and Labour.
The chief executive of HSBC has admitted that the bank "sometimes failed to live up to the standards" expected by society as it faces allegations of a major tax-avoidance scandal.
Stuart Gulliver sent a memo to staff following "painful" allegations relating to the bank's Swiss subsidiary acknowledging at times practices had not met expected standards.
Mr Gulliver wrote in the memo: "I know the recent media coverage about past practices at our Swiss private bank and the financial affairs of some of our Swiss private bank clients has been painful for you to read and watch.
"You have been working tirelessly and with great dedication to build a stronger HSBC with fully global businesses and functions, rigorous controls and the highest global standards, all underpinned by a clear strategy to serve our millions of loyal customers.
"I share your frustration that the media focus on historical events makes it harder for people to see the efforts we have made to put things right.
"But we must acknowledge we sometimes failed to live up to the standards the societies we serve rightly expected from us."
HSBC whistleblower revealing tax avoidance scandal has told ITV News that he was "never" invited to the UK despite contacting HRMC.
Labour have demanded the government makes public what they knew about the HSBC tax-dodging scandal.
The response to the HSBC scandal shows it has become harder for the rich to hide their riches, but it's still possible.