"The bank is one of a number of Swiss financial institutions supporting the ongoing negotiations between the US and Switzerland and is cooperating with the US government investigation," the bank said in a statement.
Julius Bär said it could not comment on the indictments nor give further information about the US probe after local reports and judicial sources said that the two worked for the bank.
On Tuesday, the US Attorney's Office of the Southern District of New York charged Daniela Casadei and Fabio Frazzetto with "conspiring with US taxpayer-clients and others to hide more than $600 million in offshore accounts and to evade paying US taxes on those accounts."
It did not name the bank involved, describing it simply as "Swiss Bank No. 1."
According to the statement on the US Attorney's Office website, the two bankers helped US taxpayers to open and manage undeclared accounts using fictitious names such as 'Hydrangea' and 'Red Rubin.'
They ensured that mail relating to the accounts would not be sent to the United States, and required their clients to travel to Switzerland if they had business about the accounts, it said.
They also allegedly told their clients that the accounts would remain hidden because the bank "had a long tradition of bank secrecy and no longer had offices in the United States."
Both bankers face a maximum term of five years in jail, and a top fine of $250,000 if convicted.
Switzerland has come under close scrutiny in the United States for its bank secrecy laws and has faced several tax evasion cases innvolving other banks.