* 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.