* Market starting to focus on debate on rate hike timing
* U.S. three-year auction sale also pressuring prices
NEW YORK, June 10 (Reuters) - U.S. benchmark 10-year yields rose to a one-month high 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.
For some market participants, this year's U.S. government bond market rally, which saw benchmark 10-year yields plunge to 11-month lows, may have run its course.
The $62-billion sale of new coupon-bearing government debt, which starts on Tuesday with the auction of U.S. three-year notes, has also weighed on prices. The U.S. Treasury will sell $28 billion in three-year notes later in the session.
But the Fed's two-day monetary policy meeting next week has garnered more attention. Analysts said there could be a re-assessment 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 St. Louis Federal Reserve Bank President James Bullard, who is a non-voter on the Federal Open Market Committee. Bullard said the 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.
"As the Fed continues to move closer towards its goals of full employment and 2 percent inflation, the discussion will increasingly focus on the timing of the first rate hike," said Allan von Mehren, chief analyst, Danske Bank in Copenhagen.
"We believe this is going to attract more attention in coming quarters and that there will be a further re-pricing of the U.S. money market curve, as the market is too complacent currently when it comes to timing and pace of Fed rate hikes."
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 now believe the Fed won't start shrinking its massive balance sheet before it lifts rates.
In mid-morning trading, benchmark 10-year notes were last down 7/32 in price to yield 2.642 percent, from 2.603 percent late on Monday. Yields hit a one-month high of 2.651 percent.
U.S. 30-year bonds fell 13/32 in price to yield 3.472 percent, from 3.439 percent late Monday.
Later in the session, the U.S. Treasury will sell three-year notes. That will be followed by the sale of $21 bln in 10-year notes on Wednesday, and $13 billion in 30-year bonds on Thursday.
(Editing by Nick Zieminski)