Two-year yields dropped the most in one day since May, to the lowest level since July, as traders reduced expectations the Federal Reserve will raise interest rates further in 2019.
Trading volume was light ahead of Tuesday's Christmas holiday. The US bond market shut early at 2 p.m. EST (1900 GMT) and will stay closed on Tuesday.
A partial US government shutdown that began on Saturday heightened anxiety among traders and fund managers and likely will stoke demand for this week's $113 billion of coupon-bearing Treasuries, analysts said.
"It doesn't help things at all," Mike Lorizio, head of Treasuries and agencies trading at Manulife Asset Management, said of the government shutdown. "We are seeing a classic flight-to-quality move into Treasuries."
Mick Mulvaney, the White House budget director and acting chief of staff, said on Sunday the partial federal government shutdown could continue into January as Democratic lawmakers and President Donald Trump hit an impasse over the latter's demand for funding for a border wall.
Analysts said other developments in Washington have eroded investor confidence in stocks and other risky assets.
News that Trump privately discussed the possibility of firing Fed Chairman Jerome Powell and the surprise resignation of Defense Secretary Jim Mattis also have roiled financial markets.
Trump continued his criticism of the Fed. On Monday, he said in a tweet, "The only problem the economy has is the Fed."
US Treasury Secretary Steven Mnuchin spoke on Sunday with the heads of the six biggest US banks to confirm they have enough cash to lend following the biggest weekly drop of the benchmark S&P 500 index since the Great Depression.
Mnuchin's call caused confusion, instead of soothing financial markets as intended, analysts said.
"That begs the question is there something going on?" said Chris Ahrens, chief market strategist at First Empire Securities. "The perception of (Mnuchin's call) is not helpful."
The benchmark 10-year Treasury yield was down more than 5 basis points at 2.7365 percent after touching 2.7330 percent, which was the lowest since April 2, Refinitiv data showed.
The two-year yield declined 8 basis points for its steepest daily fall since May 29. It hit 2.5470 percent, the lowest since July 9.
The gap between two-year and 10-year yields narrowed to 8.9 basis points, the tightest level in over a decade, before bouncing back to 17.7 basis points, the widest in three weeks.
The Treasury sold $40 billion in two-year notes to soft investor demand due to that maturity's drop in yield in recent weeks.
The Treasury will auction $41 billion of five-year debt on Wednesday and $32 billion in seven-year securities on Thursday.