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Morch has been responsible for the bank's Baltic operations since 2012.
Chairman Ole Andersen said it was clear that the bank should have undertaken more thorough investigations of the issues at an earlier point.
"Such investigations would have led us to understand the full extent of the issues sooner and prompted swifter actions," Andersen said.
"We have discussed this situation with Lars Morch over the last few weeks".
Andersen said last month that it was unsatisfactory that the bank may have failed to meet expectations for anti-money laundering measures in Estonia.