Nonfarm payrolls rose by 224,000 jobs last month, the most in five months, the Labor Department data showed. Economists polled by Reuters had forecast payrolls rising 160,000 in June.
The closely watched employment report led investors to scale back bets of a 50 basis point rate cut by the central bank at its policy meeting on July 30-31.
However, moderating wage growth and mounting evidence that the economy was slowing sharply could still encourage the Fed to cut interest rates by a quarter point.
"It is still more likely than not that the Fed will cut rates but the odds have decreased somewhat," said Scott Brown, chief economist at Raymond James in St. Petersburg, Florida.
"The 50 basis point cut should be priced out completely at this point."
Wall Street's main indexes have rallied to record levels on hopes of a looser monetary policy from the Fed and other major central banks in the wake of a slowdown in global growth.
Shares of banks, which tend to benefit from higher interest rates, rose 0.76pc and helped drive a 0.24pc gain in the financial sector, which was the only major index in the positive territory.
The defensive sectors - real estate, utilities and consumer staples - shed more than 1pc each as a rise in US Treasury yields made the dividend paying companies less appealing.
At 9:39 a.m. ET the Dow Jones Industrial Average was down 120.80 points, or 0.45pc, at 26,845.20, the S&P 500 was down 16.27 points, or 0.54pc, at 2,979.55 and the Nasdaq Composite was down 44.01 points, or 0.54pc, at 8,126.22.
Trading volumes are likely to be thin at the end of a holiday-shortened week as markets were shut on Thursday for Independence Day holiday.
The Philadelphia chip index slipped 1pc after Samsung Electronics Co Ltd forecast a steep plunge in its second-quarter operating profit, as a supply glut and rising tariffs hit global demand for electronics.
Qualcomm Inc slipped 1.5pc, while Intel Corp and Advanced Micro Devices Inc also fell.
Declining issues outnumbered advancers for a 3.32-to-1 ratio on the NYSE and for a 2.02-to-1 ratio on the Nasdaq.
The S&P index recorded nine new 52-week highs and no new low, while the Nasdaq recorded seven new highs and 11 new lows.