(Adds comment, U.S. three-year note auction results)
* Market starting to focus on rate-hike timing
* Tepid response to U.S. three-year auction
NEW YORK, June 10 (Reuters) - U.S. benchmark 10-year yields scaled one-month peaks on Tuesday, as investors have started to price in the prospect of higher interest rates following recent upbeat U.S. economic data and hawkish comments from Federal Reserve officials.
Some market participants believe this year's U.S. government bond market rally, which has seen 10-year yields sink to 11-month lows, may have run its course.
This week's sale of new coupon-bearing government debt, which kicked off on Tuesday with the auction of three-year notes, also weighed on prices.
But the Fed's monetary policy meeting next week has garnered more attention. Analysts said there could be a reassessment of the timing of the first U.S. rate increase.
"The Fed's bias could likely shift to a more hawkish stance. They're a little worried about financial exuberance and a little bit of complacency in the market," said Aaron Kohli, interest rate strategist, at BNP Paribas in New York.
"I think the Fed is looking to shake that complacency next week. To that end, the market is selling off a little bit."
The most pronounced change came on Monday from the president of the St. Louis Federal Reserve Bank, James Bullard, who is a non-voter on the policy-setting Federal Open Market Committee. Bullard said falling U.S. unemployment rate, together with other encouraging economic data, could prompt him to move forward his view on when interest rates should be raised.
The latest Reuters poll showed the majority of Wall Street's top bond firms don't see the Fed raising interest rates before the second half of next year, and most also believe the Fed won't start shrinking its massive balance sheet before it lifts rates.
In late trading, 10-year notes were down 3/32 in price to yield 2.634 percent, from 2.603 percent late on Monday. Yields hit a one-month high of 2.651 percent.
U.S. 30-year bonds fell 10/32 in price to yield 3.467 percent, from 3.439 percent late Monday.
Tuesday's auction of three-year notes was met with tepid reception, with rates coming slightly higher than market expectations before the sale.
Indirect bidders, which include major central banks, were awarded 26.5 percent, below the 28.1 percent last month and the 33.7 percent average.
"We'll attribute the limited interest in 3s to the smaller-than-average rollover demand and the generally bearish trend in Treasuries over the last couple weeks," wrote CRT Capital in a research note.
Next up would be the sale of $21 billion in 10-year notes on Wednesday and $13 billion in 30-year bonds on Thursday.
Overall, Treasuries have had a below average volume day at 85 percent of the 10-day moving average, said CRT.
(Editing by Leslie Adler)