"We must learn from this crisis and avoid further damage to the bank," Weber told the Blick in a joint interview with UBS chief executive Sergio Ermotti.
"We are in the process of improving the control systems," he said.
His comments came as a separate report charged that UBS had not only manipulated global interest rates, but had also tampered with Swiss franc interest rates for more than a decade.
UBS did not immediately respond to requests for comment.
US, British and Swiss authorities last week hit Switzerland's largest bank with $1.5 billion in fines — the second-largest banking penalty ever — for massive misconduct in the setting of the Libor rate.
That rate is used as a benchmark for global financial contracts worth about $300 trillion and affects financial products worldwide such as student loans and mortgages.
Both Weber and Ermotti stressed in Sunday's interview that Swiss investigators had found no indication top UBS executives were aware of the misconduct.
But Weber acknowledged that responsibility for the Libor scandal lay "not only with the people who committed crimes, but also with those who were tasked with supervising them," noting that people not directly involved in manipulating rates had also been fired.
The French-language daily Le Matin meanwhile reported in its Sunday edition that UBS had not only contributed to manipulating global interest rates on the dollar, the British pound and the yen.
It also "systematically played with interest rates on the Swiss franc. And that for more than 10 years," Le Matin reported.
Quoting findings in a US justice department probe, the paper said there was evidence that UBS traders had manipulated the rates from 2001.
The paper criticized Switzerland's financial regulator FINMA for not looking further back than 2007 when it calculated UBS's misdeeds in Switzerland, and also lambasted the Swiss national bank for not releasing numbers on how much the bank had cost the Swiss economy.
The Swiss portion of the bank's massive fine amounted to just 59 million francs ($64 million).