But von Koskull said on Thursday that the bank had already launched an internal investigation into banking procedures.
"We have started a review of our private banking operations to make sure that policies are followed, but not only policies, external tax rules are followed, also that any anti-money-laundering regulation is followed," von Koskull said as reported by Swedish Television News.
The CEO communicated that the bank's review would seek to uncover "any other potential offshore structure that may be in other parts of the bank."
"I have said and I say it now again: we do not accept that the bank is used as a platform for tax evasion," von Koskull said. "We can not be a means for tax hiding or tax evasion for any of our clients."
Nordea has cut ties with the Panama-based law firm Mossac Fonseca, which von Koskull said had not done its job properly.
Swedish Television's investigative news show "Uppdrag Granskning" found a document that indicated the bank had held a meeting about tax evasion in 2013. That would seem to refute the bank's claim that new procedures were established in 2009.
At the press conference von Koskull said that new guidelines did take effect in 2009 and if employees of the bank had not followed them, the internal investigation would bring that to light.