That survey found that the economy added 114,000 jobs in September, the fewest since June. Most of the job growth came in service businesses such as health care and restaurants.
The Labor Department raised its job-creation figures by a total of 86,000 jobs for July and August. The July figure was revised from 141,000 to 181,000, and the August figure from 96,000 to 142,000.
Taken together, the two surveys suggest the job situation in the United States is better than was thought.
Economist Joel Naroff, president of Naroff Economic Advisors, called the strong employment reports "a shocker" that showed the job market was sturdier than most economists had thought.
Financial markets seemed less impressed. The Dow Jones industrial average climbed as much as 86 points in early trading but drifted lower for most of the rest of the day. It finished up 34 points at 13,610. The Standard & Poor's 500 index, a broader measure, was down a fraction of a point.
Stock indexes have been trading at or near their highest levels since December 2007, the month the Great Recession began. They have gotten a lift from Federal Reserve efforts to stimulate the economy, and by a European Central Bank plan to buy the bonds of financially troubled countries to ease a debt crisis there.
The yield on the benchmark 10-year U.S. Treasury note climbed by 0.06 percentage point to 1.73 percent, a sign that investors were more willing to embrace risk and leave the relative safety of the bond market.
The unemployment figures were so surprisingly strong that some pundits and at least one member of Congress, Florida Republican Allen West, accused the Obama administration of manipulating the statistics to help the president's prospects.
On Wednesday, Obama was widely seen as having lost his first debate with Romney.
Jack Welch, the retired former CEO of General Electric, said on Twitter: "Unbelievable jobs numbers ... these Chicago guys will do anything ... can't debate so change numbers."