The U.S. 10-year Treasury note yield, which moves inversely to the bond's price, fell to 1.734 percent, after closing at 1.764 percent on Friday. This is down from 2.3 percent at the start of the year, as safe-haven buying has continued to weigh on yields.
Two-year note yields fell to 0.782 percent after rising earlier in the day.
Meanwhile, the longer-dated 30-year yield fell to 2.611 percent after finishing at 2.636 percent in the previous session.
Manufacturing and non-manufacturing figures from the Institute of Supply Management, due Tuesday and Thursday respectively, will also be closely watched, as will Friday's jobs report.
Friday's jobs report, which is the last big piece of data ahead of the Fed's March meeting. U.S. markets could also be sensitive to global reactions to Chinese PMI manufacturing data Tuesday.
China's central bank, the People's Bank of China, has cut further the reserve requirement ratio, the amount of cash the country's banks have to hold, in an attempt to calm investor jitters over the world's second-largest economy.
The PBOC cut the ratio by 0.5 percentage points after the country's markets closed Monday. The cut, which comes into effect Tuesday, means that most large Chinese banks will have a reserve ratio of 17 percent, Reuters reported.