Yields on 10-year Treasurys were at 2.2332 percent on Tuesday, after closing at 2.225 percent on Monday.
Meanwhile, 30-year bond yields traded at 2.9703 percent after ending at 2.949 percent in the previous session. Three-year notes yielded 1.2309 percent.
The Treasury Department on Tuesday sold $45 billion of one-month bills at an interest rate of 0.235 percent, the highest since October 2013. It also auctioned 1-year bills at a rate of 0.74 percent, the highest since November 2008.
Earlier, crude prices edged up from nearly seven-year lows on Tuesday as China reported strong commodity imports despite economic weakness but, overall, the market remained weak due to global oversupply compounded by the Organization of Petroleum Exporting Countries' decision to keep output high.
Brent futures and U.S. crude both fell more than 5.5 percent the previous session to reach 2015 lows, and they are closing in on levels last seen during the credit crunch of 2008 and 2009. Should they break through those lows, the next downward target would be levels not seen since the early 2000s.