Swiss and U.S. officials have met in recent days in Berne, Switzerland, to try to end a long-running dispute over wealthy Americans using secret Swiss accounts to dodge taxes, and they seem to be getting closer to a deal, two newspapers reported Sunday.

The fact that Michael Danilack of the U.S. Internal Revenue Service traveled to Berne for the first time to meet Swiss negotiator Michael Ambuehl was seen as a positive sign.

That shows the U.S. has a considerable interest in the negotiations and that a breakthrough seems possible, an unnamed Swiss diplomat told the NZZ am Sonntag newspaper.

Mario Tuor, a representative of the Swiss secretariat for international financial affairs, confirmed the talks had taken place, but declined to comment further, beyond saying more negotiations were planned.

The NZZ am Sonntag and the SonntagsZeitung newspaper said the negotiators were seeking a deal for the whole Swiss banking industry, as well as the 11 banks under formal investigation over allegations they assisted tax evasion.

They include Credit Suisse, Julius Baer, and Basler Kantonalbank.

The Swiss want the investigations dropped in return for payment of fines and the transfer of hundreds, or even thousands, of names of clients suspected of tax evasion, but have been haggling over how to do this given strict bank-secrecy laws.

The SonntagsZeitung cited an unnamed source as saying negotiators are seeking two parallel deals, one for the 11 banks under investigation, and a separate one for the industry as a whole, which would levy a punitive tax on undeclared assets.

In 2009, Swiss authorities reached a deal for UBS to pay a fine of $780 million to avert criminal charges, and ultimately agreed to allow the bank to reveal details of about 4,450 clients.

(Reporting by Emma Thomasson; Editing by David Hulmes)