Pressure mounted on Sunday on the chairman of UBS to step down after the Swiss bank was engulfed in a storm of criticism over its handling of a U.S. probe into tax fraud.

The Sonntag newspaper said it had surveyed the 246 members of the upper and lower houses of parliament and 23 said they wanted Peter Kurer to go, while 16 of them also thought Chief Executive Marcel Rohner should step down.

I am disappointed by the whole UBS leadership. Communication is lacking. The top management no longer feels what moves the people. Peter Kurer should take the consequences, Thomas Hurter from the Swiss People's Party (SVP) told the paper.

Philipp Mueller, a parliamentarian from the pro-business Free Democrats, said Philipp Hildebrand, vice-president of the Swiss National Bank who masterminded a rescue package for UBS in October, would be the perfect replacement.

Hildebrand is an absolutely trustworthy figure. He is highly competent ... and has precise and razor-sharp analysis, he said, adding his view was shared by the rest of his party.

However, the newspaper noted Hildebrand had been a candidate to replace former chairman Marcel Ospel when Kurer took over in April last year, but had not had enough support on the board.

A UBS spokesman rejected reports in Swiss newspapers on Sunday that suggested that Kurer and Rohner had been aware of illegal offshore structures, saying neither U.S. nor Swiss authorities were accusing them of this.

The assertion that Mr Kurer or Mr Rohner knew about tax fraud via offshore structures is false, he said in a statement, noting that the Swiss financial regulator had concluded that top UBS management had no knowledge of fraudulent business.

NO END TO BANK WOES

UBS agreed on Wednesday to pay a $780 million fine and hand over some client names to settle U.S. criminal charges.

But U.S. authorities said on Thursday they were still pursuing a civil case seeking access to 52,000 more names of U.S. citizens it says are hiding assets in secret Swiss bank accounts.

The news pushed UBS shares down to record lows on Friday, dampening hopes the settlement of the criminal case would end uncertainties hanging over the troubled company, which has made more writedowns in the crisis than any other European bank.

The UBS spokesman added that since the agreement with the U.S. authorities no new documents or facts had come to light.

How much longer, Kurer? asked the mass-circulation Blick tabloid on Saturday, noting that Kurer was warned about irregularities in the U.S. offshore business in 2006 when he was the bank's general counsel.

But Eugen Haltiner, head of the Swiss financial regulator, defended the UBS chairman.

Our investigations have shown that Mr Kurer acted immediately when he became aware of this situation as head of legal and compliance. He acted responsibly. That can be confirmed, he told the Neue Zuercher Zeitung on Saturday.

The irregularities within the bank were a failing of a few people in a company of 75,000 employees rather than a general problem, Haltiner added.

(Editing by Chris Pizzey and Jon Loades-Carter)

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