The benchmark 10-year Treasury yield fell to its lowest in more than a moth at 2.05 percent, down about 4 basis points on the day. It tumbled about 7 basis points on Monday as U.S. stock markets fell.
The two-year yield was 2 basis points lower at 0.65 percent.
Coming up on the quarter's end, people are realizing that they are under exposed to Treasurys and fund managers are "chasing performance," said Dan Heckman, national investment consultant at U.S. Bank.
"People, in general, are concerned about an overall potential for slowdown and those odds have gone up internationally and perhaps domestically."
Asian stock markets fell sharply on Tuesday after data the previous day showing a sharp fall in Chinese industrial company profits renewed concerns about the outlook for the world's number two economy.
Read MoreGlobal stocks tumble: Commodities lead the slump
European markets were lower, while U.S. stocks were slightly higher.
While the timing of U.S. rate increases remained in focus for the bond market, analysts said the prospect of higher rates was so far having a limited impact.
On Monday, New York Federal Reserve President William Dudley said the central bank remains on track for a likely rate rise this year, while San Francisco Fed President John Williams also signalled support for monetary tightening.
Read MoreFed's Dudley: Fed will likely raise rates later this year
"Despite a steady flow of Fed speak arguing for a rate rise ahead, bond yields are refusing to move higher," analysts at Rabobank said in a note.
"Two-year U.S. Treasury yields are now at 0.67 percent, which is where we started 2015; and 10-year yields are down 10 basis points since Friday's intra-day peak to 2.10 percent, the lowest since mid-August," they said.
U.S. home prices rose 5 percent in July, according to the latest S&P/Case-Shiller Home Price Index.
The September consumer confidence index came in at 103, well above the expected 96.1 estimate.