By Min Zeng 

Investors sold Treasury bonds Wednesday as a labor-market report brightened the U.S. economic-growth outlook, sapping demand for safe assets.

In recent trade, the benchmark 10-year note's price fell by 10/32, extending the price loss to a second straight session. The note's yield rose to 2.601%, according to Tradeweb. Bond yields rise when their prices fall.

Private-sector employment in the U.S. increased by 281,000 in June, according to the national employment report compiled by payroll processor Automatic Data Processing Inc. and forecasting firm Moody's Analytics. Economists had expected 210,000.

The report came before Thursday's nonfarm payrolls release, a key gauge of employment and one of the factors influencing the Federal Reserve's monetary-policy outlook.

"There is no doubt it is a very good number and the market is now pricing in a better-than-expected NFP," said Jason Rogan, managing director of U.S. government bond trading in New York at Guggenheim Securities LLC. "The 24-hour window is creating a rush to sell" Treasury bonds, he said.

Economists expect the U.S. economy added 215,000 jobs last month following 217,000 new hires a month earlier. The unemployment rate is expected to stay at 6.3%.

Dan Mulholland, head of U.S. Treasury trading at BNY Mellon Capital Markets LLC, cautions the correlation has been "loose" between the ADP and NFP reports.

Mr. Mulholland said if Thursday's report showed 300,000 jobs growth, Treasury bonds would sell off more and the 10-year yield would climb above 2.7%.

Traders and analysts said a strong employment report Thursday likely raises anxiety over whether the Fed may raise interest rates sooner than many investors currently expect. Economists expect a strong rebound of the economy for the second quarter following a 2.9% contraction during the first three months of the year amid a harsh winter.

Still, Mr. Mulholland said the Fed needs more evidence of strong reports before altering the current path of dialing back monetary stimulus at a measured pace. He cited tame wage pressure, which has given the central bank some breathing room not to rush to raise rates.

Many analysts expect the Fed to start raising rates at the middle of 2015.

Fed Chairwoman Janet Yellen said last month that the central bank may need to keep official interest rates low for an extended period. Some analysts said the Fed would tolerate inflation running slightly above its 2% target to promote stronger employment.

The 10-year Treasury yield, used to set interest rates for global finances from U.S. home loans to debt sales by foreign governments and companies, has dropped from 3% at the start of the year.

Investors have piled into Treasury bonds due to uneven global growth, geopolitical tensions in some countries and ultralow official interest rates from major central banks. U.S. bonds offer superior yields compared with their counterparts in Germany and Japan.

Many bond bears believe that Treasury yields will rise in the second half of the year, driven by stronger growth and higher inflation. Goldman Sachs Group Inc. and J.P. Morgan Chase & Co. expect the 10-year note's yield to rise to 3% at the end of December.

Write to Min Zeng at min.zeng@wsj.com

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