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.
He added that he was apologising "for lack of controls and the practices which... With the benefit of hindsight we would not be at all comfortable with if they were happening today and which have clearly resulted in damage to trust and confidence in HSBC."
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Gulliver 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.