But David Bagley, the head of compliance for London-based HSBC Holdings, told a Senate investigations panel that he will remain at HSBC.
Bagley and other current and former executives of the bank apologized for lapses but said they weren't fully aware of illicit transactions flowing through the bank.
Senators expressed skepticism that they didn't know about problems that persisted for seven years.
A report by the panel, the Senate Permanent Subcommittee on Investigations, also found that U.S. regulators knew the bank had a poor system to detect problems but failed to take action.
Bagley has been the head of compliance since 2002, during the period in which the Senate investigation found that HSBC's lack of oversight allowed the bank to be used by drug traffickers and possible financiers of terrorist groups, and for other illicit purposes around the globe.
Bagley said he lacked full authority over the bank's far-flung affiliates, which each had their own compliance officer.
"HSBC has fallen short of our own expectations and the expectations of our regulators," Bagley testified.
He said he had told HSBC senior management "that now is the appropriate time — for me and for the bank — for someone new to serve as the head of group compliance."
The executive who headed HSBC's Mexican affiliate in 2007 and 2008 said he tried to clean up deficiencies he found in the operation.
"I believe that we made real progress at HSBC Mexico during my short tenure," Paul Thurston told the panel. However, he added, "We know we should have done this better, sooner."
The executives said the bank has made deep changes to its policies and corporate culture to prevent illicit use of the bank. HSBC, which is Europe's largest bank, changed its senior management last year.
Sen. Carl Levin, a Michigan Democrat, the subcommittee's chairman, challenged Thurston. "This is something that people knew was going on at that bank," Levin said. "Why did people allow it to continue?"
Thurston said the Mexican bank, which HSBC had acquired in 2002, had been a "fast-growth" bank that lacked controls against money laundering.
Sen. Tom Coburn of Oklahoma, the panel's senior Republican, said he found it hard to believe that HSBC executives didn't know what was going on.
The CEO of the U.S. division of HSBC also apologized for weak oversight at the bank.
Irene Dorner, president and CEO of HSBC Bank USA, said in testimony prepared for the hearing that "we deeply regret and apologize" for the lapses by HSBC.
The changes the bank made "'will be embedded and sustained going forward," Dorner said.
Levin said HSBC's new policies "are all good steps."
However, he said, while apologies are welcome, "accountability for past conduct is essential. And that is what is missing here."
Levin said HSBC needs to identify which of its affiliates pose a high risk of problems and put them under close monitoring. The bank should consider closing the account of its Mexican affiliate, he said.
HSBC also should close its accounts with banks suspected of providing funding to terrorist groups, Levin said.
Some HSBC bank affiliates skirted U.S. government bans against financial transactions with Iran and other countries, according to the subcommittee's report. And HSBC's U.S. division provided money and banking services to some banks in Saudi Arabia and Bangladesh believed to have helped fund al-Qaida and other terrorist groups, the report said.
The U.S. Justice Department said it is conducting a criminal investigation into HSBC's operations but declined to confirm that the bank is in settlement talks.
HSBC's net income last year was $16.8 billion. It operates in about 80 countries around the world. Its U.S. division is among the top 10 banks operating in the United States. It has assets of roughly $210 billion in its U.S. operations.
Money laundering takes profits from the trafficking of drugs, arms or other illicit activities and passes them through bank accounts to disguise the illegal activity.
Levin also blasted the federal agency supervising the bank's U.S. operations, the Office of the Comptroller of the Currency. He said the agency "tolerated" HSBC's weak controls against money laundering for years.
Thomas Curry, who heads the Office of the Comptroller of the Currency, also was to testify at Tuesday's hearing.
Compliance with anti-money laundering laws "is crucial to our nation's efforts to combat criminal activity and terrorism," Curry said in a statement. He said the agency expects banks to have adequate programs in place to comply with the laws.