Activist investor Carl Icahn said he may seek to shake up leadership at American International Group Inc. after Chief Executive Officer Peter Hancock rebuffed his plan to split the insurer into three companies.

Icahn plans a consent solicitation that could allow shareholders to propose the addition of a new director “who would agree in advance to succeed Mr. Hancock as CEO if asked by the board to do so,” Icahn said in a letter on his website Monday.

The letter intensifies a conflict with AIG that began in late October when Icahn disclosed a stake in the New York-based company and mocked Hancock for failing to meet his return targets. Hancock has said AIG benefits from having a diversity of operations and that separating would be harder than Icahn thinks because of regulators and credit-rating firms.

“In all of our discussions with Mr. Hancock it was abundantly clear to us that he is not willing to take the bold steps that we, and so many other shareholders, believe are long overdue,” Icahn said. “He failed to lay out any alternative strategic plan with the potential to unlock value for shareholders or to provide compelling reasons as to why these businesses belong together.”

The insurer rose 33 cents to $62.54 at 9:33 a.m. in New York trading. That compares with $60.92 on Oct. 27, the day before Icahn sent a letter urging the company to split into three separate entities.