Bond yields move inversely to prices.
"Bullard's comments will probably linger in the back of everybody's minds until that meeting statement comes out," said Edward Acton, Treasury strategist at RBS Securities in Stamford, Connecticut.
Analysts also said this week's anticipated corporate supply put pressure on U.S. Treasurys prices as traders prepared to buy corporate bonds.
"If there are corporate deals that are coming to market, people have to hedge that interest rate risk" by selling some Treasurys, said George Goncalves, head of U.S. rates strategy at Nomura Securities International in New York.
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Analysts said trading volumes were low in quiet summer trading without any U.S. economic data on tap during the trading session, while reduced concerns over Greece's economy dampened demand for safe-haven Treasurys.
"We're in the summer doldrums," said Acton of RBS.
Greece reopened its banks and started the process of paying off billions of euros owed to international creditors on Monday in the first signs of a return to normal after a deal on a new package of bailout reforms.
U.S. three-year note yields were at 1.094 percent, from a yield of 1.053 percent late Friday. U.S. two-year note yields were at 0.702 percent, from a yield of 0.670 percent late Friday.
Three- and two-year note yields earlier hit their highest levels since July 2 of 1.099 percent and 0.706 percent, respectively.
Benchmark U.S. 10-year Treasury note yields were at 2.371 percent, from a yield of 2.349 percent late Friday. U.S. 30-year Treasury bonds were yielding 3.103 percent.
That marked a rise in yield from earlier in the session, when the yield hit its lowest level in one and a half weeks, at 3.066 percent.