U.S. government debt prices touched session lows in early trading on Tuesday in advance of a $32 billion auction of three-year supply, which is part of this week's $72 billion quarterly refunding.

Three-year notes last traded down 1/32 in price with a yield of 0.3223 percent, while benchmark 10-year debt last traded down 11/32 for a yield of 1.94 percent, up nearly 4 basis points from late on Monday.

The Treasury Department will conduct the three-year auction at 1 p.m.