Public Policy News and Research said the case relates to the illegal transfer of $7.5 billion out of Russia through Bank of New York accounts to a shell company owned by one of its former employees.
In 2005, the bank admitted its oversight procedures had failed and it agreed a $14 million settlement with the United States.
Lawyers representing the Russian Customs Committee argue that this amounts to an admission of guilt and they want damages under the US Racketeering Influenced and Corrupt Organizations (Rico) act, which is normally used to recover money from organized crime gangs.
The Wall Street bank contests that the statutory window for new legal actions linked to the case has closed.
Bank of New York Mellon operates in 34 countries worldwide and has around $1.1 trillion worth of assets under its management.