Pressure across the insurance industry to slim down was highlighted this month when MetLife Inc, the largest U.S. life insurer, said it would split a substantial portion of its U.S. retail business due to the "regulatory environment."

AIG's near collapse in 2008 and the government bailout that followed drove regulators to consider some non-bank companies as "too big to fail."

A break-up of the company would remove that regulatory burden. Icahn also believes this would allow AIG to return $20 billion in capital to shareholders without affecting credit ratings, the Wall Street Journal reported in October. 

Sticking to AIG's stance, Non-Executive Chairman Douglas Steenland said in the statement: "A full break-up in the near term would detract from, not enhance, shareholder value."

Icahn was not immediately available for comment. In November, he disclosed a 3.4% stake in AIG, making him the insurer's fifth-largest shareholder, according to Thomson Reuters data.