Democrats, who've been subdued in recent months amid sluggish jobs reports, lauded the news.
"Today's report marks the 31st consecutive month of private-sector job growth. While we continue to add jobs, it is imperative that Republicans and Democrats work together to ensure that our fiscal house is in order and our economic recovery remains on track," Sen. Bob Casey, D-Pa.., the chairman of the Joint Economic Committee of Congress, said in a statement.
GOP presidential candidate Mitt Romney and other Republicans said the jobless rate was still too high.
"This is not what a real recovery looks like. We created fewer jobs in September than in August, and fewer jobs in August than in July," Romney said in a statement.
At a campaign stop in Virginia, Obama accused Romney of downplaying good news. He said the jobs report "certainly is not an excuse to try to talk down the economy to score a few political points."
During his own campaign swing later in Abingdon, Va., Romney suggested that there was less to the numbers than met the eye.
"So it looks like unemployment is getting better, but the truth is, if the same share of people were participating in the workforce today as on the day the president got elected, our unemployment rate would be around 11 percent. That's the real reality of what's happening out there."
Friday brought an unusual controversy over the numbers.
Jack Welch, the iconic business guru and former head of General Electric, who supports Romney, all but accused the Obama administration of cooking the books on economic statistics to boost the president's prospects for re-election right after he fared poorly in the kickoff presidential debate earlier this week.
"Unbelievable jobs numbers," Welch said on Twitter. "These Chicago guys will do anything ... can't debate so change numbers."
Labor Secretary Hilda Solis, appearing on CNBC, dismissed the allegation as "ludicrous," and Keith Hall, a former commissioner of the Bureau of Labor Statistics, also took issue with the charge.
"People shouldn't think at all there is any bias in the numbers," said Hall, who's now a senior scholar at George Mason University's Mercatus Center. "This data is collected and examined by each state. Hundreds of people at BLS help collect this data and compile it. If you wanted to try to mess with these numbers, you are talking a very difficult thing. It almost certainly would ... be next to impossible."
A drop of three-tenths of a percentage point in the jobless rate wasn't unusual, Hall said, and any smaller change isn't considered statistically significant.
On the face of it, there was nothing untoward in the numbers. The number of people who reported that they were employed 873,000 as measured in the household survey rose by a large number over the number of people who reported that they were unemployed during the month, 456,000. In September, 12.1 million Americans reported that they were jobless.
The sharp drop in the unemployment rate jumps out, however, because it wasn't accompanied by a similarly large increase in the BLS numbers for employment. But employment and unemployment are measured on different surveys. The employment numbers are measured by the establishment survey of employers. The unemployment numbers, a smaller and more volatile sample, are gathered in a survey of households.
"Sometimes they'll give conflicting messages and sometimes it takes a month or two to resolve it," Hall said, noting that the household survey results were consistent with an increase in the size of the labor force.
Statisticians revised the earlier estimates of jobs created in July and August upward by a combined 86,000. It suggests that there's a little more tail wind in the economy than previously thought, and it corresponds with better indicators of consumer confidence and manufacturing activity.
"This was a solid employment report, given the broader sense of fragility gripping the economy. The unemployment rate fell while hours worked and earnings rose," Neil Dutta, the head of economics for Renaissance Macro Research, wrote in an investment note. "Typically, we put more weight on establishment employment than household employment. However, the strength in the household survey offset the tepid private-sector employment growth in the establishment survey."
Yet in a sign that the economy remains below par, the number of long-term unemployed - those jobless for 27 weeks or more - remained stuck in September at 4.8 million. These long-term unemployed Americans accounted for 40.1 percent of all the jobless.
The health care sector drove employment during the month, adding nearly 44,000 jobs. On the downside, the labor-intensive manufacturing sector shed 16,000 jobs during the month.
"While there were upward revisions to nonfarm payrolls in July and August and increased overall employment in September, the larger story is one of continued weakness. U.S. job growth has been dismal since February, and manufacturers' employment has declined for two months in a row," Chad Moutray, the chief economist with the National Association of Manufacturers, said in a blog post. "With slowing global growth and uncertainties about the domestic fiscal situation paramount in many minds, the prospects for future growth in the economy are shaky at best."
Job sectors in September by the numbers
Health care, up 43,500.
Transportation and warehousing, up 17,100.
Professional and business services, up 13,000.
Financial services, up 13,000.
Leisure and hospitality up 11,000.
Government jobs, up 10,000.
Retail, up 9,400.
Construction, up 5,000.
Temporary help services, down 2,000.
Manufacturing, down 16,000.
Source: U.S. Labor Department