AIG would pay out $690 million in buying out public shareholders in the insurer. The deal offers 21st Century shareholders a 19% premium to Wednesday's closing price.
AIG said it has no interest in selling its stake in 21st Century.
"Our proposal represents an excellent opportunity for 21st Century's shareholders to monetize their investment at a full and fair value for their shares," AIG said. "For AIG, this is an opportunity to make a substantial additional investment in a business we know well."