TREASURIES-Bond prices fall as investors choose stocks

* Bonds take a back seat as investors buy stocks

* $21 billion auction attracts lackluster demand

* Market at support around 3.12 percent area (Recasts, updates prices, comment)

By Ellen Freilich

NEW YORK, July 13 (Reuters) - U.S. Treasuries fell on Tuesday as a stock market rally spurred by stronger-than-expected results from Alcoa drew investors away from safe-haven U.S. government debt.

The results from Alcoa Inc (AA.N), the top U.S. aluminum producer, drove optimism about the economy and fueled risk appetite.

"It's the old familiar 'stocks up, bonds down' story with stock prices rallying -- after a very good week last week -- on better-than-expected earnings results for Alcoa," said Cary Leahey, an economist for Decision Economics in New York.

"The Alcoa news is commodity based and that supports the so-called risk trade -- at the expense of the safe-haven trade that favors bonds," he said.

And because aluminum is used in a wide variety of products, Alcoa's solid earnings signaled that demand was holding up, Leahey said.

"Good news for the economy is usually bad news for bonds," he said.

The benchmark 10-year note US10YT=RR was down 18/32 in late afternoon trade, its yield rising to 3.12 percent from Monday's close of 3.06 percent.

The Dow .DJI and the S&P 500 index .SPX each rose about 1.5 percent and the Nasdaq index climbed 2 percent.

One consequence of investors' tolerance for riskier assets was weaker demand for a $21 billion Treasury auction of 10-year notes, the second of this week's three auctions worth a total of $69 billion. Demand was also tepid for Monday's three-year offering.

The auction of a re-opened 10-year issue was "mildly weak" compared to more robust reopenings seen in recent months, said William O'Donnell, head of U.S. Treasury strategy at RBS Securities in Stamford, Connecticut.

Analysts said support for the 10-year note lay near 3.12 percent, 3.18 percent and 3.33 percent.

The 30-year Treasury bond US10YT=RR fell nearly a point, down 28/32 in late trade, its yield rising to 4.10 percent from 4.06 percent on Monday.

Two-year Treasury notes US2YT=RR were unchanged, yielding 0.67 percent, anchored at a low level by the Federal Reserve's ongoing commitment to keep interest rates near zero for an extended period. (Additional reporting by Burton Frierson; Editing by Leslie Adler)