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Treasury Dept auctions $12 billion of 30-year bonds at a high yield of 2.475%

U.S. government debt prices held lower after the Treasury Department auctioned $12 billion in 30-year bonds at a high yield of 2.475 percent on Tuesday.

The bid-to-cover ratio, an indicator of demand, was 2.13, below a recent average of 2.33.

Indirect bidders, which include major central banks, were awarded 57.9 percent, below a recent average of 62 percent. Direct bidders, which include domestic money managers, bought 4.6 percent, also below a recent average of 10 percent.

In midday trading, 10-year Treasury note yield hit a session high of 1.752 percent, while the yield on the 30-year Treasury bond was hit a high of 2.488 percent. The 10-year note yield last sat near 1.7307 percent, while the 30-year bond yield was near 2.46 percent.

The yields on the 5-year and 2-year Treasury notes also hit highs of 1.27 percent and 0.814 percent, respectively. Bond yields move inversely to prices.

The German 10-year bund yield also neared a session high of 0.072 percent, its highest level since June 23.

U.S. Markets Overview: Treasurys chart

Markets had been choppy on Monday as concerns of a possible interest rate hike in September by the U.S. Federal Reserve added volatility to markets both in the U.S. and overseas.

However, U.S. stocks ended the session sharply up on Monday, after Fed Governor Lael Brainard said it would be wise for the U.S. central bank to keep monetary policy loose. Meanwhile Atlanta Fed President, Dennis Lockhart said a "serious discussion" on raising rates was warranted at the Fed's next meeting.

However, international markets remained cautious on Tuesday as oil continued to add pressure to markets.

Along with increased oil drilling activity in the U.S., oil prices came under pressure after the International Energy Agency warned in its latest report that markets would have to wait "a while longer" for the oil market to rebalance.

Crude prices were deep in negative territory on Tuesday, with U.S. West Texas Intermediate last standing around $44.92 per barrel, while Brent hovered at $47.08.

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— CNBC's Gina Francolla and Christopher Hayes contributed to this report.