Activist investor Carl Icahn is putting more pressure on American International Group Inc. to break itself into three separate companies.

Icahn said Monday on his website that after speaking with AIG CEO Peter Hancock several times, Hancock remains unwilling to split the insurer up. Icahn vowed to reach out to shareholders directly and said he may propose adding a new director who would agree to succeed Hancock as CEO if asked by the board to do so.

AIG confirmed Monday that it is maintaining an "active dialogue" with Icahn. AIG said that it has considered breaking the company up, but that the maneuver, "did not make financial sense."

Last month, Icahn said AIG was "too big to succeed," a play on the phrase "too big to fail," which was used during the financial crisis to explain why the government was forced to prevent the total collapse of AIG. It was reasoned at the time that the collapse of AIG would have a cascading effect, dragging down other companies entangled in the growing financial crisis.

The U.S. bailed out AIG at a cost of $85 billion, money the company has since repaid. However, it has had to cut its business dramatically to focus on its core insurance operations.

Icahn said Monday that he owns more than 42 million shares of AIG, which would give him a more than 3 percent stake in the New York company.

Shares of AIG rose 34 cents to $62.55 in early trading Monday.