WASHINGTON — Service companies, which employ 90 percent of the U.S. work force, expanded at a slower pace in November and a measure of employment at those firms fell.

Separately, the government said orders to U.S. factories dropped for the second straight month.

Monday’s data show that the economy remains vulnerable despite recent signs of improvement. Still, economists said the broader message from other reports is that economic growth and hiring continue at a modest and steady pace.

“As it comes at a time when all the other economic news has been quite good, it is not too much to worry about,” said Paul Dales, senior U.S. economist at Capital Economics.

The Institute for Supply Management said Monday that its index of service-sector activity dropped to 52 from 52.9 in October. Any reading above 50 indicates expansion. The service sector has grown for two straight years. But the reading was the lowest since January 2010.

There were some positive signs in the report: New orders and business activity rose.

The trade group of purchasing managers surveys a range of industries, including hotels and restaurants, financial services, construction and agriculture.

The Commerce Department said companies cut their orders to U.S. factories in October for the second straight month. A key measure of business investment also declined.

The report also wasn’t all bad. Manufacturers boosted their stockpiles 0.9 percent in October after more modest increases in previous months. That suggests they are optimistic about future sales.

Manufacturing has been showing signs of rebounding after slowing earlier this year. Auto sales and production are up now that supply chain disruptions caused by the earthquake in Japan have eased. And the ISM, which reports separately on manufacturing, said last week that factory output expanded in November for the 28th straight month.

Some economists were surprised that the ISM service-sector survey showed its employment index fell below 50 for the second time in three months. That’s a sign that companies are cutting workers, which conflicts with other data on hiring.

On Friday, the government said the unemployment rate fell to 8.6 percent last month, the lowest level in 2½ years. Employers added 120,000 net new jobs and more jobs were generated in September and October than the government previously estimated. Half of those jobs added in November were at retailers, bars and restaurants — all service firms.

“We hope this is a rogue number,” said Ian Shepherdson, an economist with High Frequency Economics, referring to the ISM employment index for service firms. “It is certainly not consistent with the decline in jobless claims and the rebound in the flow of new online help-wanted ads, but we cannot yet be sure.”