TREASURIES-Bonds down on surprisingly high core inflation

(Updates prices, adds comments)

* Core inflation still running too high for Fed's comfort

* Fed policy meeting in focus

* Supply a key factor for Treasuries this week

* Weak economy keeps 10-year yield below 4 percent

By John Parry

NEW YORK, Aug 4 (Reuters) - U.S. Treasury debt prices fell on Monday after a higher-than-expected reading of core inflation and as traders braced for the Federal Reserve's policy setting meeting and supply of longer maturities later this week.

Yet the benchmark 10-year Treasury note's yield remained below 4 percent and not far above two-week lows, on the impression of U.S. economic fragility underscored by Friday's weak U.S. jobs report.

Among the personal income, consumption and prices data on Monday, "the focus seems to be on the inflation side (of the data) which was firm," said Josh Stiles bond strategist and managing director with IDEAglobal in New York.

The prospect of this week's issuance was also weighing on U.S. government bond prices, traders said, with the Treasury Department planning to sell $17 billion of 10-year notes and $10 billion of 30-year bonds later this week.

"The Treasury market right now is going to be driven by people involved in the auctions looking for an excuse to cheapen things up," Stiles said.

The benchmark 10-year Treasury note US10YT=RR's price, which moves inversely to its yield, traded down 10/32 for a yield of 3.98 percent, versus 3.94 percent late Friday.

The U.S. core PCE price index for June rose 0.3 percent, above economists' forecast for a rise of 0.2 percent. The core year-over-year rate was 2.3 percent, above the Federal Reserve's presumed comfort zone. Headline PCE inflation was running at 4.1 percent year-over-year. During recent months as food and energy costs have stayed high, the U.S. central bank has increasingly focused on headline measures of inflation as well.

The Federal Reserve's policy setting meeting is on Tuesday, with few expecting any shift of the fed funds target rate from the current 2 percent.

"Nobody expects anything grand from the Federal Open Market Committee, so I think this week will be supply dominated," said William O'Donnell, head of U.S. interest rate strategy and research with UBS in Stamford, Connecticut.

"This constant drone of relatively weak economic data both here and abroad as well as the continued stress in the banking system are all apparently putting a floor underneath prices here despite the supply," O'Donnell added.

Bond traders were also keeping one eye on stocks for any revival of the safe haven bid into Treasuries and out of riskier assets such as stocks. U.S. stock futures were pointing to a lower opening.

The two-year Treasury note's price US2YT=RR traded down 2/32 for a yield of 2.54 percent, versus 2.50 percent late Friday.

The 30-year Treasury bond traded down 15/32 in price for a yield of 4.60 percent US30YT=RR, versus 4.57 percent late Friday. (Reporting by John Parry; Editing by Theodore d'Afflisio)