WASHINGTON — The United States added a solid 171,000 jobs in October, and more than a half-million Americans joined the work force, the latest signs that the uneven economic recovery is gaining strength once again.

In addition, more jobs were added in August and September than believed. But the unemployment rate inched up to 7.9 percent because not all those joining the work force found work, the government said Friday.

The report was the final snapshot of the economy before the presidential election.

“The economy is in a lot better shape than most people believe,” said Joel Naroff, president of Naroff Economic Advisors. “That sets us up for stronger growth next year no matter who is elected on Tuesday.”

A government survey of households found that 578,000 Americans joined the work force in October, the Labor Department said. Of those, 470,000 found work. The difference is why the unemployment rate rose from 7.8 percent in September.

Home prices are finally rising, and retailers and car companies this week reported stronger sales. Consumer confidence in October reached its highest point in almost five years, and stocks are within reach of record highs.

Big businesses are still cautious, partly because of slowing global demand for their goods. But the report found that they continued to add jobs in greater numbers than they did last spring.

A second government survey, of large companies and government agencies, yielded the 171,000 number. Companies added 184,000 jobs, the most since February, and federal, state and local governments cut 13,000.

The report was compiled before Superstorm Sandy struck the East Coast earlier this week and devastated many businesses. Some economists think the rebuilding in the Northeast will add to construction jobs in the months ahead.

The government also revised its data to show that 84,000 more jobs were added in August and September than previously estimated. August’s job gain was revised to 192,000 from 142,000, and September’s to 148,000 from 114,000.

For the third time since the recovery from the Great Recession began in June 2009, the economy appears to be picking up momentum.

Since July, the economy has created an average of 173,000 jobs a month. That is up from an average of 67,000 a month from April through June.

The pickup in hiring suggests that businesses aren’t as worried as many analysts thought about the package of tax increases and spending cuts known as the “fiscal cliff” that will take effect unless Congress acts by Jan. 1.

Companies have cut back spending on computers, industrial machinery and other heavy equipment in recent months. That was seen by many economists as a sign of concern about the cliff and Europe’s economic deterioration.

But better consumer demand may be encouraging employers to hire more employees anyway. James Marple, an economist at TD Bank, said hiring could take off next year if the fiscal cliff is avoided.

“The fact that businesses are continuing to expand even with huge fiscal uncertainty means that once this cloud lifts, the pace of job creation has lots of room to accelerate,” he said.

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