The boss of HSBC, which is at the centre of claims that it helped customers at its Swiss private bank avoid millions of dollars of tax, called the allegations "painful" on Friday.
In a memo to staff, chief executive Stuart Gulliver added that "we sometimes failed to live up to the standards the societies we serve rightly expected from us.".
The claims in the "SwissLeaks" case emerged after a whistleblower took files from Europe's biggest bank and passed them to French authorities.
Details were published in the media this week, with the files claiming that London-based HSBC's Swiss division helped clients in more than 200 countries dodge taxes on accounts containing $119 billion (104 billion euros).
"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," Gulliver wrote in the staff memo.
"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."
Meanwhile, it emerged that the Bank of England could investigate the allegations.
Deputy governor Jon Cunliffe told the BBC it was "not yet" at the stage of calling an investigation but said the claims could be "of relevance" to the bank's Prudential Regulation Authority.