U.S. bond prices extended early gains after two economic readings showed unexpected weakness.
U.S. 0.2% in May, compared to the 0.2 percent increase expected. A separate report showed factory activity in New York state contracted in June, a sign that manufacturers are held back by a strong dollar and cutbacks in investment by oil and gas drillers.
U.S. Treasurys started the week on a firm note on Monday as jitters about Greece boosted the appeal of safe-haven bonds, pushing yields broadly lower.
Talks between cash-strapped Greece and its creditors for much-needed aid in return for reforms collapsed at the weekend, taking Athens a step closer to a debt default that could end with its exit from the single-currency zone.
The benchmark 10-year Treasury yield, which moves in the opposite direction to the price, was trading at 2.35 percent, down from 2.38 percent in New York on Friday and well off an eight-month high at 2.500 percent hit on Thursday.
Yields were lower across the curve, falling in line with their German counterparts. In contrast, the yield on the benchmark Greek 10-year bond rose sharply to about 11.8 percent while the stock market in Athens tumbled more than 5 percent as Greek jitters took a toll.
"The default scenario is going to catch more fuel during this week unless the creditors offer debt relief as part of the package and significant changes are made by the Greek sides so that the creditors feel comfortable with their new offer," Naeem Aslam, chief market analyst at AvaTrade, said in a note.
On the domestic front, attention in the bond market was expected to turn to the U.S. Federal Reserve's two-day meeting that kicks off on Tuesday.
The Fed is not expected to make any changes to monetary policy this week but its post-meeting statement is likely to be scrutinized for clues on whether it will deliver a rate hike in September.
Wall Street shares fell while the dollar was touch firmer against the euro and yen.