Robert Benmosche, the newly appointed chief executive officer of American International Group Inc , says he expects the bailed-out insurer to be able to repay its federal debts and to boost value for shareholders, according to a report by Bloomberg News.

Shares rose strongly after the report, rising as much as 31 percent on the New York Stock Exchange.

At the end of the day, we believe we will be able to pay back the government and we hope we will be able to do something for our shareholders as well, Benmosche said in an interview with Bloomberg while on holiday in Croatia.

My first charge is to get the company to operate at the level it used to operate, being the world's best, he said, according to the report. The fact is we owe the U.S. government a lot of money and we are not going to be able to pay it back just by our profits, so we will sell some of the company off but only at the right time at the right price.

An AIG spokeswoman was not immediately available for comment.

Benmosche told employees at an August 4 meeting that he planned to rebuild AIG's profitable insurance operations. I don't liquidate things, I build them, he said at that meeting, according to Bloomberg.

The new chief earlier this week halted the auction of an investment advisory unit.

Benmosche, 65, took up the CEO post on August 10. He had previously been CEO of MetLife Inc , the largest U.S. life insurer. He came out of retirement to take AIG's helm.

His task at AIG is to repay more than $80 billion in loans from the U.S. Federal Reserve and Treasury while keeping AIG stable.

AIG, once the world's biggest insurer, was saved from bankruptcy by a federal bailout last September. The company was on the verge of collapse from massive losses on derivatives linked to the subprime mortgage crisis.

SHARE REVIVAL?

I think the CEO's comments mentioned in the Bloomberg story triggered a rally this morning, said Frederic Ruffy, option strategist at Web site WhatsTrading.com.

AIG shares were up $7.02 26 percent at $33.66 in late morning trading. Earlier they hit $35.00, their highest level since a one-for-20 reverse stock split on July 1, according to Reuters data.

In the options market, traders exchanged about 216,000 contracts or nine times the normal number in the first 90 minutes of trade, according to option analytics firm Trade Alert.

Out of that volume, 125,000 call options -- granting the right to buy the shares at a fixed price within a specified time period -- changed hands.

There is heavy trading in August $30 and $35 call strikes which expire at the end of this week, indicating that many investors are looking for today's rally in AIG shares to continue in the short term, Ruffy said.

Ruffy also noticed active trading in the September $14 puts where investors, paid a premium of 25 cents per contract and were possibly buying some insurance in case AIG should run into trouble again.

As its financial problems set in last year, the value of AIG shares sank dramatically, and the bailout resulted in taxpayers getting a nearly 80 percent stake, heavily diluting shareholders.

(Reporting by Lilla Zuill; Editing by Lisa Von Ahn and Gerald E. McCormick)