Stronger-than-expected job growth of 288,000 in June sparked talk that the Fed could move sooner to raise interest rates, but central bank watchers say the underlying job market is still too weak to change the Fed's course.
Stocks moved higher, with the Dow crossing 17,000 for the first time ever at the opening bell. Bond yields backed up, with the 10-year yield moving 0.5 to 2.67 percent. The two-year, which reflects attitudes about short-term rates, touched 0.52 percent, its highest level since September.
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"Clearly what the bond market is telling us supports the idea the economy is accelerating and ultimately, the Federal Reserve is on the right course winding down its asset purchase program," said Daniel Greenhaus, global market strategist at BTIG.
Capital Economics said in a note that the strength in the labor market is one of the key reasons it believes the Fed will be persuaded to begin raising interest rates earlier than most expect.
The unemployment rate fell to 6.1 percent from 6.3 percent, its lowest rate since September 2008. Economists had expected just 215,000 jobs and an unchanged unemployment rate. Revisions to April and May payrolls data showed an increase of 29,000 more jobs during those months.
June's job growth caps five straight months of 200,000-plus job gains for the first time since late 1999. According to Greenhaus, it is the sixth best five-month period for total job growth since 2000.
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"This is a good job market by any historical standard," said Moody's Analytics' chief economist, Mark Zandi.
He said the Fed has a list of job indicators, including long-term unemployment, it will be watching and the picture is still not strong enough to speed up the Fed's return to normalcy. "I think they need confirmation over the next three- to six-month period that we've jumped to this higher rate of job creation," Zandi said.
The Fed has been tapering back its bond-buying program in $10 billion increments, and it is expected to wind down the program in the fourth quarter. After that it would consider when to begin raising short-term interest rates.
"It's a long way before the Fed meets to raise interest rates. I think it will be by this time next year. That's the current forecast. We're not going to get jobs numbers like today in every number going forward," said Zandi.
Average hourly earnings rose by 0.2 percent, for a 2 percent increase year over year. The level of labor force participation, or share of working age Americans employed or looking forward, was unchanged at its post-recession low of 62.8 percent.
The number of long-term unemployed, out of work 27 weeks or longer, fell by 293,000 to 3.1 million. Fed Chair Janet Yellen has expressed concern about this group, which totals about a third of all unemployed and has the hardest time finding jobs.
"We're generating jobs by the bushel," said Ward McCarthy, financial economist at Jefferies. "Some of the things Janet Yellen is looking at are improving but they're not good enough. ... They're at distressed levels. They're still worse than we've seen in prior recessions."
"One fly in the ointment is the composition of the household survey. There was a big increase in part-time employment and decrease in full-time employment," he said.
Part-time workers increased by 275,000 in June to 7.5 million. The number of discouraged workers in June was 676,000, down 351,000 from the year earlier.
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—By CNBC's Patti Domm