Bank of New York Mellon's new Chairman and Chief Executive Gerald Hassell vehemently defended the bank's actions as both a foreign-exchange trader and as a trustee that reached a watershed settlement for mortgage-bond investors.

Hassell, speaking at the Barclays financial conference in New York in his first public appearance as head of the nation's biggest custody bank, said the bank would fight claims that it had unfairly charged some customers on foreign exchange. Hassell also said BNY Mellon would defend charges of negligence...