NEW YORK, Jan 31 (Reuters) - Bangladesh's central bank sued a Philippine bank on Thursday to recoup losses it suffered when unidentified hackers stole $81 million from its account at the Federal Reserve Bank of New York nearly three years ago.

In a complaint filed with the U.S. District Court in Manhattan, Bangladesh Bank accused Rizal Commercial Banking Corp (RCBC) and other defendants of involvement in a massive, multi-year conspiracy to steal its money, much of which disappeared in the Philippines' casino industry.

"We welcome this complaint, as it is an opportunity for RCBC to put on record again that it was a victim of what was started in Bangladesh by still unnamed persons," RCBC said on Wednesday, after learning that a lawsuit would be filed. (Reporting by Jonathan Stempel; Editing by Sandra Maler)