TREASURIES-Bonds climb with safe-haven support

* Bonds' safe-haven appeal bolstered by weaker stocks

* Decent demand seen in Tuesday's two-year note auction

* Consumer confidence data also supports bond prices (Adds strategist's comments, updates prices)

By Chris Reese

NEW YORK, July 28 (Reuters) - U.S. Treasury debt prices rose on Tuesday, with the 30-year bond more than one point higher, as stocks retreated, taking back some recent gains and bolstering the safe-haven appeal of government debt.

Weaker-than expected consumer confidence this month also helped bonds and offset any bearish impact of data showing a surprise rise in U.S. home prices in May.

Despite the price gains, investors nervously awaited the auction of $42 billion of two-year Treasury notes on Tuesday afternoon as part of a record $115 billion in new debt supply this week.

"People are rebalancing a little bit in favor of Treasuries," said David Dietze, chief investment strategist with Point View Financial Services in New Jersey. "Treasuries are looking over their shoulder at stocks, which have had a spectacular two-week run."

The benchmark 10-year Treasury note US10YT=RR was trading 21/32 higher in price for a yield of 3.64 percent, down from 3.72 percent late on Monday, while 30-year bonds US30YT=RR were trading 1-18/32 higher for a yield of 4.53 percent, down from 4.63 percent late on Monday.

Many analysts expect relatively solid demand in the two-year note auction, as the security's shorter maturity makes it less susceptible to economic uncertainty while still offering a higher rate than even shorter-dated Treasury bills.

"The two-year is expected to go off without a hitch because it is the optimal part of the curve," said William Larkin, fixed income portfolio manager at Cabot Money Management in Salem, Massachusetts.

The Treasury will auction $39 billion of five-year notes on Wednesday, and $28 billion of seven-year notes on Thursday. It sold $6 billion of 20-year inflation-protected securities on Monday, bringing this week's total coupon sales to $115 billion.

Treasury prices also found support on Tuesday from data showing U.S. consumer confidence fell by more than expected in July, with sentiment hobbled by a difficult job market. For details see [ID:nN28406937].

"With the consumer being two-thirds of the economy, if they are in a bad mood, that certainly bodes poorly for consumer spending," Point View's Dietze said, adding "that sends negative vibrations for the outlook for the economy and Treasuries are the key safe haven."

The market showed little impact from the home price index of Standard & Poor's/Case Shiller, which showed prices in 20 metropolitan areas rose by 0.5 percent in May after falling 0.6 percent in April. Investors had been looking for May home prices to decline by 0.5 percent.

For some analysts, the home prices were more evidence that the U.S. housing sector may be pulling out of its sharp decline, adding to data on Monday showing higher-than-expected new-home sales in June.

"It's largely consistent with the bottoming process in the housing sector," Tom Porcelli, senior economist at RBC Capital Markets in New York.

Two-year Treasury notes US2YT=RR were trading unchanged in price for a yield of 1.05 percent, while five-year notes were 10/32 higher for a yield of 2.52 percent from 4.63 percent late on Monday. (Additional reporting by Richard Leong; Editing by Kenneth Barry)