COPENHAGEN (Reuters) - U.S. authorities are closely following an investigation into Danske Bank DANSKE.CO over allegations that Denmark's biggest lender had been involved in money laundering through its Estonian branch.

Danske Bank sign is seen at the bank's Estonian branch in Tallinn, Estonia August 3, 2018. REUTERS/Ints Kalnins

Investors are watching for signs of a possible U.S.-led fine, which would be another big hit to the bank, which has seen its shares fall by more than a fifth over the past six months as the scandal has unraveled.

“We are following this case very closely,” Assistant Secretary for Terrorist Financing at the U.S. Department of the Treasury, Marshall Billingslea, told Danish daily Berlingske.

He declined to confirm whether U.S. authorities had started an investigation into Danske Bank, which is being probed in both Denmark and Estonia.

“But we have a close cooperation with the authorities here in Denmark, as well as in Estonia,” he told the newspaper.

A Danske spokesman declined to comment on a potential dialogue between the bank and U.S. authorities.

“It is completely natural that there is interest for the case in Estonia from different authorities, including the U.S.,” he said in an emailed comment to Reuters, adding that the bank is making information available to authorities if needed.

The bank has admitted to flaws in its anti-money laundering controls in Estonia and has launched its own investigation, the results of which are expected in September.

Estonian and Danish prosecutors have started criminal investigations concerning transactions worth billions of Danish crowns that might have been part of criminal money laundering.

While the bank does not have a banking license in the United States, it has a bond program in dollars and its Estonian branch saw U.S. dollar customer flows, which could heighten interest among U.S. regulators.

For now, analysts on average put estimates for potential fines at roughly 4 billion Danish crowns ($628 million).