TREASURIES-Weak stocks, decent auction ignite bond rally

* Lower stocks keep investors bidding for bonds

* Market relieved after mixed $35 bln, 3-year auction

* 10-year notes up for auction next on Wednesday (Updates with latest gains in 30-year bonds)

By Burton Frierson

NEW YORK, July 7 (Reuters) - U.S. Treasuries prices rose on Tuesday, pushing benchmark yields to six-week lows, as weak stocks enhanced the allure of safe-haven government debt and investors cheered a decent auction of three-year notes.

Some measures showed strong demand at the auction but market sentiment took a temporary hit from indications that dealers bid more aggressively than expected to get the bonds at a lower price, based on the yield.

After a brief post-auction setback, Treasuries resumed their rally on the back of Wall Street's weaker tone, which often sends investors scurrying into the safety of government bonds.

"The weakness in the equity market provided a little bullishness to bonds," said Frank Hsu, director of global fixed income at Fimat in New York.

"We were not expecting a good auction but it came out all right. So it's kind of a relief."

The benchmark 10-year Treasury note US10YT=RR was last up 18/32 in price, pushing the yield down to 3.45 percent from 3.52 percent at Monday's close. During the session, the yield fell as far as 3.44 percent, the lowest since May 26, according to Reuters data.

The 30-year long bond US30YT=RR also rallied, rising more than a full point in late New York trade.

It was last trading up 27/32 on the day, yielding 4.31 percent versus Monday's close of 4.36 percent.

The gains in longer-dated bonds were somewhat surprising given that Treasury will auction $19 billion worth of 10-year notes on Wednesday, part of the $73 billion in government bonds hitting the market this week.

On Thursday, the government will sell $11 billion worth of 30-year bonds.

Indeed, longer bonds were outperforming shorter maturities, which some said was due to growing worries about the fragile state of the U.S. economy, which remains mired in its worst recession in decades.

Underscoring the difficult task of restoring growth, the American Bankers Association said soaring U.S. unemployment and a shrinking economy drove delinquencies on credit-card debt and home equity loans to all-time highs in the first quarter. For more see [ID:nN07299679].

Such an environment often keeps inflation under wraps, which is good for fixed income investment such as bonds, and might even increase the threat of a deflationary downward spiral in prices, wages and economic activity.

"I think that we're starting to see the dial shift from inflation fears to some more concern about deflation," said Lou Brien, market strategist with DRW Trading Group in Chicago.

ON THE BLOCK

Investors will be watching this week's remaining auctions closely since longer-dated debt can be more difficult to sell.

Auctions of longer-dated bonds also are increasingly seen as tests of the government's borrowing ability.

Due to a burgeoning budget deficit to finance economic and bank bailouts, the government expects to bring $2 trillion worth of new bonds to market this year, which has weighed heavily on Treasuries in recent months.

Judging by the three-year note sale, appetite for U.S. government debt remains healthy, but shorter maturities often benefit from a wider and deeper pool of potential investors.

Overall demand measured by the bid-to-cover ratio was a brisk 2.62 times the amount on offer, well above the long-term average but below levels recorded at auctions in May and June.

Appetite among foreign investors such as central banks and large institutional buyers such as pension funds and insurance companies also posted a strong reading, based on the indirect bidding category.

Indirect bidders took more than 50 percent of the sale, well in excess of long-term averages and higher than recent auctions. (Editing by James Dalgleish)