Switzerland is set to partially meet a U.S. ultimatum and deliver an estimate of the amount of assets held by U.S. residents in secret accounts at Swiss banks, possibly up to $30 billion, a newspaper reported on Tuesday.

Citing unnamed sources, the TagesAnzeiger reported that Switzerland would hand over on Tuesday details that the FINMA financial markets regulator has gathered from banks in recent months on accounts held by Americans with more than $50,000.

According to unconfirmed estimates there were $20-30 billion from tens of thousands of clients, the paper wrote.

Newspapers reported on Sunday the United States had given an ultimatum to Switzerland, saying Credit Suisse and nine other banks could face charges unless information on U.S. tax evaders using Swiss accounts was handed over by Tuesday.

Switzerland is resisting reverting to emergency law as it did to settle a U.S. investigation against UBS when it bent strict bank secrecy laws to reveal details of some 4,450 UBS clients to avoid criminal charges.

Swiss Finance Minister Eveline Widmer-Schlumpf said on Monday Switzerland would not deliver detailed client data by Tuesday, she said: That would mean applying emergency law and we're not applying emergency law here.

I am against ultimatums. This is no way of dealing with other states, she told Swiss television.

Mario Tuor, a spokesman for the Swiss department for international financial affairs, told the TagesAnzeiger: A possible exchange of client data should take place within the framework of existing laws.

Tuor was not immediately reachable for comment to Reuters.

But the United States seems to be pushing for more than current Swiss law would allow, seeking details of all U.S. clients with accounts worth at least $50,000 between 2002 and 2010 at banks including Credit Suisse, Julius Baer and Wegelin as well as the Zurich and Basel cantonal banks.

The United States has ratcheted up the pressure on Switzerland in recent months, targeting Credit Suisse in a formal investigation and indicting a number of Swiss bankers, alleging they helped former UBS clients shift assets to other Swiss banks rather than coming clean to the taxman.

Two Swiss Sunday papers said a letter sent by U.S. Deputy Attorney General James Cole on August 31 demands detailed figures on tax evasion at Credit Suisse by Tuesday. The banks are also expected to have to pay a fine of up to 2 billion Swiss francs.

(Reporting by Emma Thomasson and Catherine Bosley; Editing by Hans-Juergen Peters)