TREASURIES-Yields slip as traders await inflation data

* Traders await CPI data for signs of persistent inflation pressures

* Fed funds futures price in 68% chance of rate hike by December

* Treasury auctions this week test investor demand amid fiscal concerns

By Karen Brettell

NEW YORK, June 9 (Reuters) - U.S. Treasury yields edged lower on Tuesday as traders awaited key consumer price inflation data for signs of whether price pressures are continuing to build. Wednesday's consumer price inflation data follows Friday's stronger-than-expected jobs report for May, which bolstered bets on interest rate hikes later this year. Fed funds futures traders are now pricing in a 68% chance of a hike by December.

May's CPI release is expected to show that price pressures slowed on the month but increased on an annual basis, with headline inflation expected to be 4.2% on the year, and core inflation 2.9%.

"The market is penciling in increased odds that the data is strong enough and inflation is strong enough that the Fed will be forced to hike rates," said Gennadiy Goldberg, head of U.S. rates strategy at TD Securities.

Optimism that the conflict with Iran may be nearing a resolution, however, has kept some inflation fears in check and helped draw demand for Treasuries.

"In the absence of a catalyst, it does seem like there is buying of Treasuries going through," said Goldberg. On Monday, Israel and Iran halted direct attacks on each other after an appeal by U.S. President Donald Trump for them to stop, but Tehran said it would resume hostilities if Israel continued to attack its ally, the Hezbollah militia in Lebanon.

The 2-year note yield, which typically moves in step with Fed interest rate expectations, fell 2.5 basis points to 4.133%.

The yield on benchmark U.S. 10-year notes fell 1.4 basis points to 4.536%.

The yield curve between 2- and 10-year notes was at 40 basis points.

Traders will also be watching demand for longer-dated U.S. debt at the Treasury's auctions this week, after a sharp selloff a month ago raised concerns that investors were getting more wary of the debt due to a worsening fiscal outlook.

The Treasury will sell $119 billion in new coupon-bearing supply, including $58 billion in three-year notes on Tuesday, $39 billion in 10-year notes on Wednesday and $22 billion in 30-year bonds on Thursday.

(Reporting by Karen Brettell Editing by Nick Zieminski)