TREASURIES-Losses reduced after stocks erase some gains

* Safety bid revives after stocks erase some gains

* July consumer confidence even lower than forecast

* Bid emerges at 10-yr 3.04 pct-3.065 pct support area

* Demand seen for $38 billion auction of two-year notes (Updates after consumer confidence report)

By Ellen Freilich

NEW YORK, July 27 (Reuters) - U.S. Treasuries prices fell on Tuesday, but some losses were cut after a gloomy reading on U.S. consumers' mood erased many of the stock market's early gains and revived the bid for safe-haven U.S. government debt.

The U.S. consumer confidence index fell to 50.4 in July from a revised 54.3 in June as consumers worried about the job market, the Conference Board said.

In the Treasury market, however, a concession was still in place for the Treasury's two-year note auction at 1 p.m. (1700 GMT) and traders said the sale would attract demand.

"Expect some consolidation around these levels (in Treasuries) with financials trading well both here and in Europe and earnings continuing positive," said John Spinello, chief fixed-income technical strategist at Jefferies & Co.

A move in the benchmark 10-year note yield to a support area between 3.04 percent and 3.065 percent also attracted a bid, technical strategists said.

TWO-YEAR NOTE AUCTION

Spinello said the Treasury's auction of $38 billion in two-year notes would not be difficult for the market to digest, especially with the concession that began overnight.

"Many are willing to keep money safe in short, liquid Treasuries given a Fed at ZIRP (short-term interest rates near zero) for the foreseeable future," he said.

The cheapening of the when-issued two-year notes from Monday's close has created a "favorable" setup for the $38 billion sale, said Thomas di Galoma, head of fixed-income rates trading at Guggenheim Securities in New York.

"The 2s are still very attractive on the rolldown," he said, referring to the interest paid on the investment in the form of accrued interest or coupon.

As technicals have turned negative for Treasuries, additional concessions should take place to absorb the rest of the week's note supply beyond the $38 billion two-year notes.

The Treasury will sell five-year notes on Wednesday and seven-year notes on Thursday.

From a technical perspective, Spinello advised selling 10-year notes when the yield moves to the 2.98 percent to 2.96 percent area and said buying could emerge when the yield moves to the 3.04 to 3.065 percent area and again at 3.10 percent.

Benchmark U.S. 10-year Treasury notes fell 12/32 on Tuesday, their yields rising to 3.04 percent from 2.99 percent late on Monday.

Spinello said the 3 percent yield on the 10-year note was merely a psychological boundary. However, foreign buyers' resolve to buy on dips is "critical," he said.

DiGaloma said the benchmark 10-year Treasury note yield climbed above 3 percent as investors reallocated funds to riskier assets following better bank earnings in Europe.

The sell-off in Treasuries continued as investors revalued financial stocks and the broader equity market.

DiGaloma expressed some skepticism about the reallocation out of Treasuries into riskier assets, however.

"We see much of the earnings surge as more of a lack of optimism by forecasters rather than simply stellar performance," he said.

DiGaloma said financial firms profited as low short-term funding costs created high net interest margins.

"Those margins are now contracting as their funds charges converge on loan resets in a lower interest rate environment," he said.

In when-issued trade, the two-, five- and seven-year notes to be sold on Tuesday, Wednesday, and Thursday, respectively, yielded 0.678 percent, 1.818 percent and 2.483 percent. (Editing by Andrea Ricci)