Treasury Department auctions $24B of 3-year notes at a high yield of 0.895%

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Bonds trimmed gains Tuesday after the Treasury Department kicked off this week's $58 billion debt supply with a three-year note offering that traders categorized as ordinary.

The Treasury auctioned $24 billion in three-year notes at a high yield of 0.895 percent, virtually in line with the when-issued yield. The bid-to-cover ratio, an indicator of demand, was 3.14 — the lowest since August 2014.

Indirect bidders, which include major central banks, were awarded 47.7 percent, below the 51 percent average.

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Direct bidders, which includes domestic money managers, bought 11.1 percent, versus a recent average of 10 percent. That was the highest level in three auctions, according to Reuters.

Shorter-dated maturities inched into positive territory after the announcement, before turning flat.

In longer-dated debt, yields on the 10-year Treasury were down 2 basis points at 2.036 percent after reaching a session high of 2.48 percent. Meanwhile, 30-year bond yields fell 2 basis points to 2.88 percent.

Benchmark 10-year note yields climbed back above 2 percent Monday, recovering from lows not seen since April, after weak services sector data, which supported the view that the U.S. Federal Reserve might hold off on raising rates this year.

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Tuesday's auction comes a day after the Treasury sold three-month bills at a rate of zero for the first time ever.

A $21 billion 10-year note auction is scheduled for Wednesday, followed by a $13 billion sale of 30-year bonds Thursday.

Traders will watch market action carefully Tuesday to see if stocks can demonstrate a successful retest of the lows ahead of what some expect to be a lackluster earnings season.

On the data front, investors digested U.S. international trade for August, which showed a gap of $48.3 billion, above the expected $47.4 billion.

U.S. stocks traded in a narrow range Tuesday afternoon, attempting to extend a two-day rally. The Dow was last up about 20 points, while the S&P 500 and Nasdaq inched lower.

— CNBC's Evelyn Cheng contributed to this report.