Chief Executive Stuart Gulliver and Chairman Douglas Flint issued the new apology in an appearance before parliament's influential Treasury Select Committee.
"I'd like to put on the record an apology from both myself and from Douglas for the unacceptable events that took place," Gulliver told the committee.
"It clearly was unacceptable," he said.
HSBC has faced outrage over claims that it helped clients from around the world dodge taxes on accounts containing 180 billion euros (USD 204 billion) between November 2006 and March 2007 which are being investigated in several countries.
The banking chief was also quizzed by lawmakers over revelations this week that he had received his HSBC bonuses through a Swiss bank account that was held by a Panamanian-registered firm and opened in 1998.
"I can understand how people find these arrangements kind of unusual," he told the committee.
Gulliver, who has worked for HSBC for 35 years and became chief executive in 2011, said he was a Hong Kong resident and intended to return there after completing his assignment in Britain.
Gulliver stressed again that he had paid UK tax on his worldwide earnings for HSBC, company dividends and sales of shares.
Asia-focused banking titan HSBC has seen its reputation tarnished in recent years by a string of high-profile controversies.
HSBC paid out USD 1.92 billion to US authorities in 2012 for oversight failures which meant Mexican drug traffickers could launder money through its accounts and banned transactions took place from Iran.
Last year, the bank was charged with manipulating a key inter-bank lending rate by the European Commission.
HSBC has also faced vast compensation claims in Britain over the mis-selling of both interest rate hedging products and payment protection insurance.
