The yield on the benchmark 10-year Treasury note was up at around 2.967 percent at 10:16 a.m. ET, while the yield on the 30-year Treasury bond was up at 3.115 percent. Bond yields move inversely to prices.

U.S. government debt yields rose after the number of job openings in the U.S. economy hit an all-time high.

Markets around the globe picked up Tuesday, as concerns surrounding trade tensions took a backseat and investors turned their attention earnings and data.

The economic data arrives just days after July's jobs report came in below market forecasts, with total nonfarm payrolls rising by 157,000, below the 190,000 predicted by economists polled by Reuters. Fresh inflation data are due out on Thursday and Friday.

Meantime, the U.S. Treasury is set to auction $70 billion in four-week bills and $34 billion in three-year notes.

Concerns surrounding trade linger on. Last week, China said it was ready to retaliate with tariffs on around $60 billion of U.S. goods, ranging from 5 percent to 25 percent, just days after the U.S. administration revealed that President Donald Trump had spoken with U.S. Trade Representative Robert Lighthizer and asked him to consider increasing the proposed levies on $200 billion of Chinese goods up to 25 percent, from 10 percent.

Chinese state media claimed in editorials over recent days that Beijing's counter-response to Washington has been "restrained" and "rational" in light of the levies that have been threatened.