(Updates with market reaction following Federal Reservepolicy-making meeting, adds byline)

By Manuela Badawy and Herbert Lash

NEW YORK (Reuters) - World stocks rallied and goldprices hit new highs Tuesday after the Federal Reserveopened the door to bolstering the struggling U.S. economy byincreasing the money supply again.

U.S. Treasury yields fell after Fed policy-makers at theend of a one-day meeting failed left short term interest ratesunchanged but said it would use all policy tools if needed tobolster a sluggish economic recovery.

The Fed also underscored its concerns over slowinginflation in its statement on Tuesday, saying the underlyingrate of inflation was below levels consistent with its mandatefor price stability and full employment.

"This sets the table for QE (quantitative easing) inNovember or December should it be necessary. They are nowoutlining the key rationale for that -- low inflation, highunemployment," said Eric Green of TD Securities.

World stocks as measured by MSCI reboundedto trade 0.3 higher after the Fed statement.

Wall Street stocks also rallied. The Dow Jones industrialaverage was up 46.85 points, or 0.44 percent, at10,800.47 late afternoon in New York. The Standard & Poor's 500Index was up 2.07 points, or 0.18 percent, at 1,144.78.The Nasdaq Composite Index was up 3.72 points, or 0.16percent, at 2,359.55.

After its August meeting, the Federal Reserve issued ableak assessment of the economy and the S&P 500 stock indextumbled more 4.0 percent over the next four days.

"The across-the-board rally is consistent with marketsseeing the Fed as both able and willing to stimulate sufficientgrowth and stable inflation," said Mohamed El-Erian, co-chiefinvestment officer at Pacific Investment Management Co., whichoversees more than $1 trillion in mostly fixed-income assets.

While stocks rallied on hopes that the Fed would boosteconomic growth, gold prices spiked to a new high on fears thatgovernment deficit spending and higher growth rates will spurinflation. Spot gold prices rose to a new record higharound $1,288.50.

The benchmark 10-year U.S. Treasury note gained28/32 in price, driving its yield down to 2.60 percent on theprospect of further Federal Reserve purchases of U.S. debt.

The U.S. dollar was down against a basket of majorcurrencies, with the U.S. Dollar Index down 1.10 percentat 80.439.

The euro was up 1.35 percent at $1.3241, whileagainst the Japanese yen, the dollar was down 0.75percent at 85.04. (Reporting by Jennifer Ablan, Rodrigo Campos, Chris Kelly,Richard Leong and Nick Olivari in New York; Writing by HerbertLash)