The two top US senators who led the investigation into Credit Suisse’s decades-long tax evasion schemes expressed concerns on Tuesday about the Justice Department’s criminal conviction of the bank.



Senators Carl Levin and John McCain welcomed the $2.6bn fine of the bank announced Monday but said more needed to be done. Levin and McCain led the permanent subcommittee on investigations team that uncovered much of the wrongdoing at the bank.



In a statement, Levin said it was “appropriate” that Credit Suisse had been held criminally liable for aiding and abetting tax evasion – the first bank of this scale to held criminally liable for 20 years.



He said the fine struck “an important blow against tax evasion through bank secrecy”.

“But it is a mystery to me why the US government didn’t require as part of the agreement that the bank cough up some of the names of the US clients with secret Swiss bank accounts. More than 20,000 Americans were Credit Suisse account holders in Switzerland, the vast majority of whom never disclosed their accounts as required by US law. This leaves their identities undisclosed, with no accountability for taxes owed. The changes Credit Suisse has agreed to make to its practices are long overdue and welcome, but must be carefully monitored,” he said.



McCain said he was “gratified” by the Justice Department’s decision to require Credit Suisse to plead guilty to criminal wrongdoing. “In such cases, it is vitally important for all Americans to know that no financial institution is ‘too big to prosecute,’” he said. But he added that questions remained.



“Over the next few days, I look forward to reviewing this guilty plea closely to see whether it appropriately holds officers, directors and key executives individually accountable and whether the plea will be sufficient to help deter similar misconduct in the future,” he said.



A number of junior executives at the bank have been prosecuted over the massive tax scam but so far no senior executives have been held accountable. At a press conference on Tuesday, chief executive Brady Dougan, who has been with the bank for 25 years, said he had never considered resigning over the scandal. "Going forward I am very committed to Credit Suisse," he said.



Dougan said the settlement had had little impact on business. “We have found no instances where clients cannot do business with us,” he said. “Our discussions with clients have been very reassuring and we haven’t seen very many issues at all.”



On Monday, attorney general Eric Holder said the scheme had involved “hundreds of Credit Suisse employees, including at the manager level” and said more prosecutions were to come. He said the bank had organised tax dodges for US citizens that ran for decades. “In the case of at least one wholly owned subsidiary, the practice of using sham entities to conceal funds began more than a century ago,” said Holder.



The criminal conviction was, however, carefully constructed in order to protect the bank from severe financial consequences outside of the fine. Nor did it call for the resignation of senior executives. Legal experts said the Justice Department was keen to avoid a punishment that would destroy the bank.



Accounting firm Arthur Andersen was convicted of obstruction of justice in 2002 in relation to its auditing of Enron, the energy firm that imploded in a massive accounting scandal. That ruling was reversed on appeal but was enough to destroy the company.



Nell Minow, board member at corporate governance analyst GMI Ratings, called the criminal convictions “a small step forward”. “This bank is a convicted felon,” she said. “This is a small step forward unless individuals are named and punished. That has to start at the very top.”



John Coffee, Adolf A Berle professor of law at Columbia Law School, said the Justice Department had consulted carefully with the Federal Reserve, the Securities and Exchange Commission (SEC) and other regulators to make sure there were “no unanticipated consequences”, resulting from the criminal conviction.



“They were making sure that in a sense this was a red carpet, cushioned landing for Credit Suisse. They don’t want anything like an Arthur Andersen-like debacle,” he said. Coffee said that this case had destroyed the idea that criminal charges would destroy a financial institution and was likely to lead to other criminal charges against other banks now being investigated by the US authorities.



“It is less than a severe sanction when no officers are indicted, when the settlement does not require the dismissal of any employees and where they do not get the names of these US customers,” he said. He said other regulators could take further action, the SEC could bar it from being a money manager, but that was not going to happen.



“Mary Jo White [chair of the SEC] does not want to inconvenience a major bank over a little thing like a federal felony conviction,” he said.



Coffee said the Justice Department wanted the Credit Suisse case to go smoothly so that it could move on to other banks, including US banks, where it has greater jurisdiction. “When they have a US bank, they will have easier jurisdiction over employees,” he said.



• This article was amended on Thursday May 22 to reflect that the senators' concerns relate to the conviction, not an indictment.