ZURICH (Reuters) - Swiss private bank Frey & Co. is to close due to "unsustainable costs" stemming from the country's dispute with the United States over alleged tax evasion, it said on Friday, making it the second Swiss bank to shut as a result of the row.

Switzerland and the United States have been at odds since 2010 over a U.S. campaign to get Switzerland's banking secrecy laws cracked open so it can identify possible U.S. tax evaders, a campaign which felled Wegelin, Switzerland's oldest bank, in January following an indictment.

Frey, which had assets under management of 1.9 billion Swiss francs ($997 million) at the end of 2012, said it was one of 14 banks ineligible for a government-struck settlement program with the U.S. Department of Justice because they are already under investigation by U.S. authorities.

It has not been indicted as part of the continuing U.S. Department of Justice proceedings and nor it is under threat of indictment, it said.

After shareholders voted to close Frey on Thursday evening the bank said increased regulation of financial institutions has resulted in a rise in costs in recent months, meaning it was no longer possible for a small private bank to keep running.

"As a result of developments in recent years, circumstances and challenges have presented themselves, especially in Switzerland, that mean it no longer makes sense for a small bank to continue its cross-border services," Chairman Markus A. Frey said in a statement

However, the business was financially healthy and would not be liquidated, the bank said.

($1=0.9029 Swiss francs)

(Reporting by Alice Baghdjian; Editing by Greg Mahlich)