The yield (which moves inversely to the price) on the benchmark 10-year Treasury note traded about flat at 1.772 percent, while the yield on the 30-year Treasury bond barely budged to 2.603 percent. The 10-year yield hit its lowest level since March 1 earlier in the session.
In prepared remarks, Boston Fed President Eric Rosengren said futures markets are wrong, and the Fed likely should hike rates sooner than they imply.
Rosengren, who is historically considered to be about as dovish as Fed Chair Janet Yellen, said he expects a strong economy and full employment. He also said he expects inflation will rise gradually.
U.S. oil prices fell nearly 3 percent, settling at their lowest level since March 4.
Fixed income investors continue to digest the dovish comments from Fed Chair Janet Yellen last week. There was a better-than-expected nonfarm payrolls number on Friday but the same data dump also showed that the unemployment rate ticked higher to 5.0 percent. There will be more Fed speak on Monday as traders look for hints on the future path of U.S. interest rates.
Other Fed speakers include Minneapolis Fed President Neel Kashkari and Dallas Fed President Rob Kaplan.
On the data front, U.S. factory orders for February fell 1.7 percent, in line with estimates.
— CNBC's Everett Rosenfeld contributed to this report.
Correction: This article has been updated to reflect U.S. crude hit a session low of $36.11.