WASHINGTON — The private sector added a disappointing 166,000 net new jobs last month and significantly revised down its estimate for August in a sign that labor market growth weakened through the summer, payroll processing firm ADP said Wednesday.

The figure for last month was below analysts’ projections that the closely watched report would show that businesses added 180,000 jobs in September.

September’s job growth was an improvement from the previous month, but only because ADP revised its August figure down to 159,000 from the initially reported 176,000.

“The job market appears to have softened in recent months,” said Mark Zandi, chief economist at Moody’s Analytics, which assists ADP with its monthly report.

The ADP figures take on added significance this month because the partial federal government shutdown probably will delay Friday’s release of the Labor Department’s September jobs report.

Economists have been projecting that report would show the economy added 184,000 net new private and public sector jobs last month, up from 169,000 in August. The unemployment rate is projected to have held steady at 7.3 percent.

The weaker ADP numbers could affect those projections.

Chris Rupkey, chief financial economist at the Bank of Tokyo-Mitsubishi in New York, called ADP’s September figure a “middle of the road” number. But ADP has not always been a great predictor of overall job growth, he said.

“This kind of leaves us high and dry on what the economy is doing,” Rupkey said of the delayed government jobs report.

ADP showed that financial services firms cut 4,000 jobs last month and the manufacturing sector remained soft, Zandi said.