NEW YORK (Reuters) - Shares of insurance giant American International Group Inc <AIG.N> rose as much as 33 percent, buoyed by the company's improving relations with former long-time CEO Maurice "Hank" Greenberg.

"I think it's the notion that there's a reconciliation underway between Greenberg and the company," said Bill Bergman, a Chicago-based senior analyst for Morningstar Inc.

AIG's new chief executive, Robert Benmosche, told Reuters in an interview that he had turned to Greenberg for help and support and has been in regular contact with him.

Greenberg, in a separate interview by phone, said, "If Bob Benmosche seeks any assistance, whatever he needs me to do, I'll be glad to give him."

Greenberg, 84, who built AIG into the world's largest insurer, resigned from the company in 2005 amid an accounting scandal and has had icy relations with the firm ever since.

Bergman said an AIG reconciliation with Greenberg could mean new private capital investment in the company, which survived the recent financial crisis only through massive government help.

"Hank Greenberg has a network of associates in financial markets that would help facilitate that," he said.

Benmosche, 65, took over on August 10 as AIG's fourth CEO in five years.

AIG shares were up $9.29 to $46.98 in afternoon trade on the New York Stock Exchange after climbing as high as $50.04 in morning dealings. The stock was at its highest levels since last October.

(Reporting by Joe Rauch and Elinor Comlay; editing by Andre Grenon and John Wallace)