The jobs report was preceded by other signs of growing economic strength, including a jump in consumer confidence, the strongest auto sales in four years, rallying stock prices and, at long last, a stabilization of housing prices.

According to the monthly survey of employers, the bulk of the gains came from service jobs, particularly in education and health care. Though government downsizing has been a drag on the recovery, government over all added 10,000 jobs in September, the third consecutive month of gains.

The nation’s employers have added an average of 146,000 jobs a month in 2012, just ahead of the numbers that are considered necessary to absorb new workers into the labor force. “This is not what a real recovery looks like,” Mr. Romney said in a statement.

Areas of weakness included manufacturing, one of the bright spots that Mr. Obama has showcased throughout the re-election campaign. It lost 16,000 jobs after a revised 22,000 drop in August in the face of a global slowdown. The number of temporary jobs, usually considered a harbinger of future growth, fell 2,000. Speaking to a rain-soaked crowd of 9,000 at Cleveland State University, Mr. Obama said, “Today’s news should give us some encouragement. It shouldn’t be an excuse for the other side to talk down the economy just to try to score some political points.”

“We’ve made too much progress to return to the policies that led to this crisis in the first place,” the president said to cheers.

The nation now has nearly the same number of jobs as when Mr. Obama took office in January 2009. Since the economy stopped hemorrhaging jobs in February 2010, there has been an increase of more than 4.3 million. A mere 61,000-job increase would allow Mr. Obama to claim a net gain in jobs over his tenure.