* Rates ease on Treasury bills due Oct/Nov

* Focus on efforts to open government, lift U.S. debt ceiling

By Ellen Freilich

NEW YORK, Oct 15 (Reuters) - Most U.S. Treasuries prices were narrowly lower on Tuesday while short-term bill rates were the lowest in a week as participants focused on efforts in Washington to re-open the government and raise the U.S. debt ceiling.

At the shortest part of the maturity curve, interest rates on U.S. Treasury bills eased amid hints of a possible agreement in Washington that would reopen the government after it was partially shut for the first time in 17 years.

Treasury rates on T-bill issues due in October to November fell to their lowest level in a week, although they remained at elevated levels compared with three weeks ago.

A month-long struggle in the U.S. Congress showed signs on Monday of giving way to a Senate deal to reopen closed federal agencies and avoid a damaging default on federal debt.

The one-month Treasury bills due on Nov. 7 US1MT=RR are the most sensitive to efforts to raise the statutory $16.7 trillion borrowing limit, on track to be exhausted on Thursday.

Rates on those short-term bills rise when a settlement of the potential crises looks in doubt and ease on hints that a resolution is nearer at hand.

The T-bill issue due on Nov. 7 last traded at 0.203 percent, down 3.5 basis points from late on Friday.

Still, the overnight general collateral (GC) rate remained significantly elevated due to the debt ceiling crisis, said John Canavan, fixed-income analyst at Stone & McCarthy Research Associates in Princeton, New Jersey.

"It is currently around 0.25 percent, and was 0.27 percent last Thursday, which was the highest the early morning GC rate had been since April 12," he observed.

News that factory activity in New York State grew in October at its most anemic pace since May had no discernible impact.

The Empire State index "is an independently surveyed sentiment gauge, not constructed from components, and was probably impacted by early reactions to the Washington confrontation," said Pierre Ellis, senior economist at Decision Economics in New York.

The Fed will purchase Treasuries in the 4.75-year to 5.75-year sector of the curve this morning.

The market opened for the first session of the week after being closed on Monday for the Columbus Day holiday.

At the longer end of the yield curve, benchmark 10-year notes US10YT=RR were last down 4/32, their yields rising to 2.70 percent from 2.695 percent late on Friday.

(Additional reporting by Richard Leong; Editing by Nick Zieminski)

((ellen.freilich@thomsonreuters.com)(+1-646-223-6309)(Reuters)( Messaging:)(ellen.freilich.thomsonreuters.com@thomsonreuters.net )(ellen.freilich@thomsonreuters.com)) 

 ((-------MARKET SNAPSHOT AT 09:25 a.m. EDT (1325 GMT)-------                                                 Change vs    Current                                           Nyk        yield Three-month bills 
  US3MT=RR
    0.060       ( unch)     0.061 Six-month bills   
  US6MT=RR
    0.080       (+0.01)     0.081 Two-year note  
  US2YT=RR
       99-25/32   ( unch )     0.358 Five-year note  
  US5YT=RR
      99-24/32   ( unch )     1.426 10-year note   
  US10YT=RR
      98-08/32   (-03/32)     2.702 30-year bond   
  US30YT=RR
      97-21/32   (-02/32)     3.756))

Keywords: MARKETS USA BONDS/