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A private trade group’s measure of the strength of the services sector shrank for the sixth straight month in March, and at a faster pace than expected, as job losses mount.

A services index from the Institute for Supply Management, a Tempe, Ariz.-based trade group of purchasing executives, fell to 40.8 last month from 41.6 in February. Economists surveyed by Thomson Reuters expected the index to edge up to 42. Any reading below 50 indicates contraction. Businesses’ new orders, which presage any recovery in hiring and production, fell to 38.8 from 40.7 in February.

“We haven’t stopped free-falling,” said Joel Naroff, president of Naroff Economic Advisors.

The report is based on a survey of the institute’s members in 18 industries. It covers such indicators as new orders, employment and inventories. About three-quarters of Americans work in service-providing industries such as hotels, retail, education and health care.

Employment shrank for the 14th time in 15 months, dropping to 32.3 from 37.3 in February. Naroff said that even when demand for goods and services recovers, firms will expand their output through overtime and temporary workers before hiring more people.

Analysts had expected the services index to rise slightly following recent modest improvements in home and car sales, and a related measure of the manufacturing sector.

The ISM on Wednesday said its manufacturing index rose to 36.3 in March from 35.8 in February. The reading beat expectations, but that sector has shrunk for 14 straight months.

The services report found that the real estate industry grew in March, while the other 17 industries contracted.

“Respondents remain concerned about the negative economic outlook and rising unemployment,” said ISM survey chair Anthony Nieves, and the services industries continued their steady decline since the first quarter of last year.

Even companies known for strong hiring, such as Google Inc., are laying people off. Google last month said it would cut nearly 200 jobs, mostly in advertising sales.

Survey respondents pinned some hopes on the Obama administration’s $787 billion stimulus package, which includes money that will flow to states for public works projects, help them defray budget cuts, extend unemployment benefits and boost food stamp benefits. The administration also is counting on programs to prop up financial companies and reduce home foreclosures to help turn the economy around. Eight of the industry sectors, including real estate, education, finance and insurance, construction and health care, said they expected to benefit from the spending.

Employers are laying off workers at a faster pace despite a few hopeful signs recently that the recession  could be easing.

The Labor Department on Friday is slated to release a report expected to show that a net total of 654,000 jobs were lost last month.

If economists are right, it would mark a record four straight months that job losses topped 600,000.

“It’s going to be another month of gargantuan jobs losses,” predicted Stuart Hoffman, chief economist at PNC Financial Services Group. “Companies were slashing jobs and not filling vacant positions.”

With employers axing payrolls, the nation’s unemployment rate is expected to jump to 8.5 percent, from 8.1 percent in February. If that happens, it would mark the highest jobless rate since late 1983, when the country was recovering from a severe recession that drove unemployment past 10 percent.

As the recession, which started in December 2007, eats into their sales and profits, companies are laying off workers and resorting to other cost-saving measures. Those include holding down hours, and freezing or cutting pay, to survive the storm.

Looking forward, economists expect monthly job losses continuing for most — if not all of — this year.

However, they are hoping that payroll reductions in the current quarter won’t be as deep as the roughly 650,000 average monthly job losses in the January-March period. In the best-case scenario, employment losses in the present quarter would be about half that pace, some economists said. That scenario partly assumes the economy won’t be shrinking nearly as much in the present quarter.

Even if the recession ends this year, the economy will remain frail, analysts said. Companies will have little appetite to ramp up hiring until they feel the economy is truly out of the woods and any recovery has staying power.

Given that, many economists predict the unemployment rate will hit 10 percent at the end of this year. The Fed says unemployment will remain elevated into 2011.

Economists say the job market may not get back to normal — meaning a 5 percent unemployment rate — until 2013.

To brace the economy, the Fed has slashed a key bank lending rate to an all-time low and has embarked on a series of radical programs to inject billions of dollars into the financial system. And the Obama administration had launched a multi-pronged strategy to turn the economy around. Its $787 billion stimulus package includes money that will flow to states for public works projects, help them defray budget cuts, extend unemployment benefits and boost food stamp benefits. The administration also is counting on programs to prop up financial companies and reduce home foreclosures to help turn the economy around.