Leaders of the nation’s largest public retirement systems said Tuesday they will ask their boards to approve suing troubled insurance giant American International Group Inc. to recover $400 million in losses suffered since the company’s problems surfaced in February.

Treasurer Phil Angelides, a board member of the $182.9 billion California Public Employees Retirement System and $125 billion California State Teachers Retirement System, said “allegations of scandal and misconduct” at AIG have caused “grievous damage” to holdings of more than 2 million California retirees and employees.