"My sense is that weve already hit the low point, with the Wegelin indictment," Donald Beyer told Swissinfo, the international branch of the national broadcaster, in an interview about bilateral relations.
US tax officials have pressured Swiss banks to release information about clients who are US nationals and who might be evading taxes and reports say 11 Swiss banks are being targeted by US authorities.
In January, three Wegelin bankers were charged in New York with conspiring to help US clients escape tax payments.
"The other banks seem eager to participate and to cooperate. In the newspapers recently you saw both Credit Suisse and Julius Bär eager to say we want to come forward and help in any way we can," said Beyer.
The ambassador said he believed banks involved in the row would turn over data if allowed to under Swiss law.
"So far they dont feel that they are allowed to and are awaiting a resolution between the two governments."
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Admitting that "there is tension," Beyer stressed that what was happening was not "an attack on Swiss banks" but rather "...an attempt to hold a couple thousand Americans who cheated on their taxes in the United States accountable for paying their taxes."
Wegelin, which was founded in 1741, announced on January 27th the sale of its non-US activities to fellow Swiss bank Raiffeisen "as a consequence of the increasingly threatening situation surrounding Wegelin & Co Private Bankers in the US tax dispute."