Billionaire 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 will push for a measure that would enable shareholders to communicate directly with the board and possibly seek the addition of a director “who would agree in advance to succeed Mr. Hancock as CEO if asked by the board to do so,” the activist investor said in a statement on his website Monday.

The statement 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 the insurer’s return targets. Hancock, who became CEO last year, has said AIG benefits from having a diversity of operations and that separating into three would be harder than Icahn thinks because of hurdles from 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.”

Icahn’s firm has more than 42 million shares of AIG, giving him a 3.4 percent stake, according to a regulatory filing Monday. That would make him the fifth-largest investor in the company, according to data compiled by Bloomberg.

‘Increased Pressure’

“Our sense is a breakup of AIG is unlikely in part because it depends on cash flows from the U.S. life and retirement- services business to support debt service and funding significant share buybacks,” Jay Gelb, an analyst at Barclays Plc, said in a note to clients Monday. “Even so, increased pressure on AIG’s board should intensify the pace of improvement and likely benefit AIG shares.”

The insurer rose 1.6 percent to $63.18 at 1:38 p.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 separate companies, one selling life insurance, another offering property-casualty protection, and the third backing mortgages.

‘Too Important’

Icahn seeks to take action through a consent solicitation, which would allow shareholders to collectively engage with the board and possibly put someone new on the board without the need for a shareholder meeting. The company’s bylaws say that written actions may be approved if a majority of the company’s shares are represented.

“AIG is too important, and the current situation is too time-sensitive, to wait years,” Icahn said in Monday’s statement. “In fact, we believe the current situation is too time-sensitive to even wait until the company’s annual meeting next spring, especially when all of the stakeholders who have reached out to us believe management’s current plan (or lack thereof) is insufficient.”

‘No Sacred Cows’

Hancock, 57, told analysts this month that there are “no sacred cows” as he seeks to narrow the company’s focus, meaning he would be prepared to sell more units after divestitures in Central America and Taiwan and the exit from an aircraft-leasing business. He said that separating life and property-casualty segments could be negative for bondholders, and reiterated that AIG has still been able to repurchase billions of dollars of stock in recent years.

The insurer said Monday that it will “accelerate its previously announced strategy” and will provide further details before reporting fourth-quarter results.

“AIG maintains an active dialogue with shareholders, including Carl Icahn,” according to a statement from AIG. “Management and the board have carefully reviewed a separation of AIG’s businesses on many occasions, including in the recent past, and have concluded it did not make financial sense.”

AIG trades for less than book value, while the stocks of many of its property-casualty insurancepeers sell for more than the measure of assets minus liabilities. The activist also said the insurer suffers from being deemed a systemically important financial institution by the U.S. government, which can add compliance costs and stricter capital rules.

Icahn cited in his October letter the support of billionaire hedge fund manager John Paulson, who also is among the largest holders of AIG. Paulson & Co. could also support a plan to sell life and mortgageinsurance assets as an alternative to spinoffs, people familiar with the firm’s thinking said earlier this month.

–With assistance from Alicia Ritcey and Brandon Kochkodin.

*This story was updated with a newer version.