Danske Bank said earlier it would forgo profits made from the transactions, which relate to a period from 2007 and 2015.

"The sin is not erased because they now acknowledge that they can't keep the money," business minister Rasmus Jarlov told Reuters in an interview.

"Whatever legal options there might be for the Danish authorities, they will pursue them," Jarlov said.

Denmark's financial watchdog said in May it had found "serious weaknesses" in Danske Bank's governance after an anti-money-laundering probe into the bank's Estonian branch.

It also ordered the bank to set aside an extra 5 billion Danish crowns ($781 million) in regulatory capital in response to the laundering allegations. Analysts estimate the bank could face potential fines in the region of 4 billion crowns.

Danske Bank has admitted to flaws in its anti money-laundering controls in Estonia and launched its own investigation into the case, which is due to present its findings in September.

(Reporting by Stine Jacobsen; Editing by Jacob Gronholt-Pedersen and Mark Potter)

By Stine Jacobsen