Chairman of the Credit Suisse board, Urs Rohner, opened a general assembly meeting in Zurich on Friday by assuring shareholders the bank was doing everything in its power to bring the crippling dispute to an end.
"The resolution of the tax dispute is one of the most pressing issues currently facing Credit Suisse," Rohner told the assembly.
Credit Suisse is one of 14 Swiss banks under criminal investigation by the US Justice Department on suspicion they helped wealth US clients hide billions of dollars in assets from tax authorities.
Switzerland's second largest bank is expected to soon be slapped with fine of at least $1 billion and could face criminal charges.
Company chief executive Brady Dougan assured the assembly that the bank's management was fully "focused on achieving a manageable outcome and putting this issue behind us".
"We certainly understand that the sooner we can get to a resolution and eliminate the uncertainty on this, the better," he said.
A damning US Senate report found that Credit Suisse at its peak in 2006 had more than 22,000 US customers with Swiss accounts whose assets stood as high as $12 billion – mainly undeclared to US tax authorities.
Chief executive Brady Dougan apologised in February to US senators for the bank's actions, conceding it had undertaken elaborate efforts to gain new, secret American clients, but blamed the wrongdoing on a small band of rogue employees.
But his words did little to calm matters, and a senior US official told AFP earlier this week the US probe of Credit Suisse was nearing an end and that criminal charges could be brought within "a few weeks".
And the Wall Street Journal reported that Credit Suisse was about to reach an agreement with the Justice Department that would see it plead guilty and pay a $1.0 billion fine.
Rohner stressed Friday that "we are doing everything we can to resolve this matter."
He insisted the bank from the start had taken the US probe "very seriously" and had been cooperating closely with US authorities to the extent it was possible without breaking Swiss law.
Washington wants Credit Suisse to hand over the names and account details of all the US clients who had had secret accounts.
But Swiss banking secrecy laws, which appear en route to extinction under increasing international pressure, block banks from handing over any information about their clients, unless the clients are individually named in an official request for judicial assistance sent to Bern.