COPENHAGEN (Reuters) - A senior Danske Bank executive quit on Thursday after the lender found there should have been an earlier and more thorough investigation into alleged money laundering at its Estonian branch.

The departure of Lars Morch, responsible for the Baltic operations of Denmark's biggest bank since 2012, comes during an internal investigation into the Estonian operations due to be completed by September.

The case is one of several highlighting alleged money laundering issues in the Baltic states as authorities clamp down on conduits for illicit funds linked to Russia.

Danske Bank Chairman Ole Andersen said he respected Morch’s decision to resign and said it was clear the bank should have undertaken more thorough investigations 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".

Danske said Morch would be released from his duties as soon as possible and he would formally end his employment at the end of October 2019. He will continue to be paid in the meantime.

The bank had been criticized for failing to take appropriate measures after a whistleblower who, according to reports in Denmark's Berlingske and Britain's Guardian, alerted the bank in December 2013 about money laundering linked to Russia through its Estonian branch.

Morch, who also received warnings from the bank's internal auditors in early 2014 about insufficient compliance at the Estonian branch, according to documents reviewed by Danish newspaper Berlingske, could not be reached for comment.

REGULATORY BREACHES

Elsewhere in the Baltic states, Latvian bank ABLV was closed in February after U.S. accusations that it was serving as a conduit for illicit funds. The bank's former management denies wrongdoing.

Latvia has also moved to ban shell companies, often used in money laundering.

The European Central Bank also last month revoked the licence of small Estonian bank Versobank over failures to remedy regulatory breaches in areas such as money laundering.

Events at Danske Bank had led to speculation over the position of Chief Executive Thomas Borgen, who headed the International Banking unit, which includes the Baltic operation, for two years before Morch assumed control and who has headed a turnaround at the group since taking charge in 2013.

A Danske spokesman said Borgen would not comment on the matter. Andersen was not available for further comment.

Leonhardt Pihl, chief executive of the Danish Shareholders Association, a lobby group for private investors, said further departures would be damaging in the short term. "But I think there's enough talented people inside Danske Bank to find new, good managers to run the bank," he added.

Estonia's FSA said on Thursday it had carried out thorough on-site inspections at the Danske branch in 2014 and 2015, which had resulted in a request to remedy legal breaches.

As a result Danske had terminated the provision of services for riskier non-resident clients in 2015, the FSA said.

"Normal supervisory cooperation between the Estonian and Danish supervisory authorities has taken place on this issue," Kilvar Kessler, chairman of the FSA management board, said in an email.

Denmark's business minister did not respond to a request for comment.

(Reporting by Teis Jensen; Additional reporting by David Mardiste in Tallinn,; Editing by Jacob Gronholt-Pedersen and David Holmes)

By Teis Jensen