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U.S. Treasury yields trimmed earlier losses which came after the Treasury Department auctioned $24 billion in three-year notes at a high yield of 1 percent.
The bid-to-cover ratio, an indicator of demand, was 3.34, higher than ten-auction average of 3.27.
Indirect bidders took 52.7 percent, up from a recent average of 42 percent, while direct bidders took 11.6 percent, which was lower than a recent average of 14 percent.
"Near the highest yield in two months, the three-year note auction was above average," Peter Boockvar, chief market analyst at The Lindsey Group, said in a note. "Bottom line, at least on the short end which is well anchored by the Fed which we know will be glacial in raising rates whenever the time comes, the current yield saw pretty good demand."
Ten-year Treasurys yielded 2.2410 percent slightly down from 2.2428 percent ahead of the auction. They most recently traded at 2.2610 percent.
Thirty-year bonds also yielded lower from 3.0018 percent to 2.9984 percent following the sale. They most recently traded at 3.0206 percent.
Three-year note yields slipped to 0.9728 percent from 0.9755 percent. They most recently traded at 0.9809 percent.
Earlier, benchmark Treasury yields resumed their climb, with 10-year note yields hitting a six-month high of 2.36 percent. Thirty-year bonds also yielded as much as 3.12 percent.
The price of U.K. Gilts fell on Tuesday, along with all major sovereign bonds in continental Europe.
"We maintain our short 10-year U.S. Treasurys versus Bund recommendation as the Federal Reserve is less likely to lean against recent developments than the European Central Bank," said Barclays Research analysts Anshul Pradhan and Vivek Shukla in a note on Tuesday.
William Dudley, president of the New York Federal Reserve and an ally of Fed Chair Janet Yellen, said on Tuesday that he did know when interest rates would rise. However, he applauded the apparent consensus between markets and the Fed that this would happen later this year.
On Wednesday, the Treasury Department will auction off $24 billion in 10-year notes, the second of three offerings this week.
Little major economic data is due during the day, with just the federal budget for April, which is seen showing an increased surplus, due at 2:00 p.m. ET.
Rising oil prices were also in focus, as Goldman Sachs warned that the rally was premature.
U.S. crude closed up 2.5 percent at $60.75.