The yield on the benchmark 10-year Treasury note traded at 2.282 percent at 2:51 p.m. ET, while the yield on the 30-year Treasury bond rose to 2.866 percent. Bond yields move inversely to prices.

U.S. government bond yields rose on Tuesday, as investors pored over more economic data.

The Treasury Department auctioned $24 billion in three-year notes at a high yield of 1.520 percent. The bid-to-cover ratio, an indicator of demand, was 3.13.

Indirect bidders, which include major central banks, were awarded 64.1 percent. Direct bidders, which includes domestic money managers, bought 10.2 percent.

Data-wise, the Bureau of Labor Statistics' Job Openings and Labor Turnover Survey (JOLTS) reported that the number of job openings increased to a record 6.2 million on the last business day of June.

The National Federation of Independent Business' (NFIB) small business optimism index hit 105.2 for July, higher than the 103.6 level in June.

While no major speeches are expected from Federal Reserve members on Tuesday, investors are likely to be mulling over the comments recently made by a Fed president.

On Monday, St. Louis Fed President James Bullard said in Nashville that the U.S. central bank wouldn't need to raise interest rates in the near term as inflation isn't expected to rise very much even if the country's job market continues to advance, .