Energy, financial, and utility shares rose on the Federal Reserve’s bullish economic outlook, helping the Standard & Poor’s 500 Index post its best two-day gain since 2003.

American International Group Inc., the world’s biggest insurer, and Citigroup Inc., the largest American bank, rallied after the Fed said losses in credit markets won’t hamper the economy’s “moderate” expansion. Exxon Mobil Corp. and Marathon Oil Corp. helped lead shares of oil and gas companies to the biggest advance since July 12.

The Standard & Poor’s 500 Index rose 9.04, or 0.6%, to 1476.71. The Dow Jones Industrial Average increased 35.52, or 0.3%, to 13,504.3. The Nasdaq Composite Index climbed 14.27, or 0.6%, to 2561.6.

“The Fed’s saying there’s no reason to panic,” said Robert Carey, who oversees $31 billion as chief investment officer of First Trust Portfolios LP in Lisle, Ill. “They know things are getting tough out there in some parts of the economy but overall we have employment growth, rising incomes, and a robust global economy.”

American shares have recouped almost one-third of the $1.6 trillion wiped out since July 13 by concern loans to risky home buyers will spread through credit markets. Ratings provider Moody’s Investors Service said earlier that the fallout from subprime-mortgage losses will be “manageable.”

The Fed kept its benchmark interest rate at 5.25%.

“Financial markets have been volatile in recent weeks, credit conditions have become tighter for some households and businesses, and the housing correction is ongoing,” the rate-setting Federal Open Market Committee said. Financial shares in the S&P 500 climbed 0.9% as a group and posted their best two-day gain since October 2002.

AIG added 99 cents to $65.55. Citigroup climbed 24 cents to $48.59.

“This is a really benign report,” said Michael Koskuba, who helps manage $59 billion at Victory Capital Management in New York. “Their largest concern is inflation but they’re also comfortable with how it looks and how the economy is, so that points to the fact that corporations are going to post strong earnings growth.”

Fannie Mae shares gained $1.93 to $64.43. Smaller competitor Freddie Mac rose $1.64 to $61.64.

Fannie Mae officials approached the Office of Federal Housing Enterprise Oversight in the past few days to have restrictions lifted so it can hold more home-loan assets in its portfolio, said a person with knowledge of the request who declined to be named because the discussions were confidential. A spokesman for Fannie Mae declined to comment.

Senator Dodd, a Democrat of Connecticut who chairs the committee that oversees the government-chartered home lenders, said yesterday that they should be allowed to increase mortgage purchases as a way to curb foreclosures.