J.P. Morgan Chase & Co.'s chairman and chief executive officer, James Dimon, renewed his apologies to shareholders for last year's multibillion-dollar trading fiasco, and an investor that has pushed for corporate-governance changes at large financial firms said it would focus this proxy season on changing the bank's board.

The developments highlight the challenges facing the largest U.S. bank ahead of its annual shareholder meeting next month in Tampa, Fla. Investors will vote on an advisory proposal to strip Mr. Dimon...