AIG chairman and CEO Maurice Greenberg said in a statement that he hoped to talk soon with American General officials about the proposal, which values the company at $46 per share.
The offer represents a premium of 25 percent from American General's closing stock price Tuesday of $36.80. American General is based in Houston, while AIG is headquartered in New York.
"We believe that the combination of our two companies is uniquely attractive, in terms of mix of businesses and distribution channels, and would be highly beneficial financially to both of our shareholder groups," Greenberg said.
On March 12, Prudential PLC offered $26.5 billion in stock to acquire American General, one of the nation's largest insurance and financial services companies. But the value has slid with its share price as investors fretted over the deal.
Based on Tuesday's closing prices, Prudential's offer now would be worth about $20 billion overall.
"It appears clear that the exceptionally steep price drop experienced by Prudential's stock reflects investors' serious concerns with the transaction," wrote Greenberg, in a letter to American General CEO Robert Devlin. AIG made the letter public late Tuesday.
Prudential is unrelated to the Newark, N.J.-based Prudential Insurance Co. of America.
John Pluhowski, an American General spokesman, didn't immediately return a telephone message seeking comment.
Prudential spokeswoman Geraldine Davies said Prudential had seen the announcement.
"We note that our merger agreement with American General remains in full force and effect," she said, declining to comment further.
American General shares fell 13 cents to $36.80 on the New York Stock Exchange on Tuesday before AIG's offer was announced while AIG fell $2.74, or 3.3 percent, to $80.21.