On the other hand, reduced trading volume because of Passover and Easter holidays this week may end up depressing bids for the $56 billion worth of coupon-bearing Treasuries, analysts said.
"You are getting some safe-haven bids on geopolitical concerns," said Guy LeBas, chief fixed income strategist at Janney Montgomery Scott in Philadelphia.
Polls released on Monday showed a tight first-round French presidential contest on April 23, led by anti-EU, anti-immigrant National Front candidate Marine Le Pen and centrist Emmanuel Macron. They indicated Macron would beat Le Pen in a May 7 runoff.
The possibility of a Le Pen victory has raised fears that France, the euro zone's second-biggest economy, might withdraw from the currency bloc.
In the Middle East, US President Donald Trump is open to additional strikes on Syria following last week's missile assault in response to civilians killed by chemical attacks by Syria's military, a White House spokesman said.
Unfounded rumors about military maneuvers in the Korean peninsula amid concerns about North Korea's advancing weapons program caused a brief dip in stock prices and bond yields to session lows, traders said.
The decline in bond yields was limited by poor demand at a $24 billion three-year note auction where the bid-to-cover ratio was the weakest since July 2009.
The US Treasury Department will sell $20 billion of 10-year notes on Tuesday and $12 billion of 30-year bonds on Wednesday.
The yield drop was also mitigated by the possibility the US central bank will begin paring reinvestments into Treasuries and mortgage-backed securities.
Earlier Monday, St. Louis Fed President James Bullard said the Fed could begin winding down its $4.5 trillion balance sheet later this year.
Wall Street's top banks see the central bank making such a move in 2017, according to a Reuters poll conducted on Friday.
Investors await further clues on balance sheet normalization from Fed Chair Janet Yellen, who will participate in a discussion on public policy at the University of Michigan at 4:10 p.m. (2010 GMT). Â The yield on the benchmark 10-year Treasury was 2.362 percent, down 1 basis point from late on Friday, while the yield on 30-year was 1 basis point lower at 2.988 percent.
US financial markets will close on the Good Friday holiday.