WASHINGTON — The private sector added 213,000 net new jobs last month, indicating that the labor market rebounded after a disappointing August, payroll firm Automatic Data Processing said Wednesday.

The September job growth was an improvement from ADP’s figure for the previous month, which it downgraded slightly to 202,000, and better than expected by economists.

The data bode well for Friday’s government report on overall September job growth. Economists expect the Labor Department to report that the economy added 215,000 net new jobs and that the unemployment rate held steady at 6.1 percent.

“All the leading indicators for the job market look good,” said Mark Zandi, chief economist of Moody’s Analytics, which assists ADP in preparing the report.

But the firm, whose monthly report is closely watched by economists, significantly undershot the government’s 142,000 job-growth figure for August.

Economists believe that slowdown was an anomaly and expect the numbers to be revised up by the Labor Department. Zandi said he expected revisions to boost August job growth close to 200,000.

Based on the ADP figures, Zandi forecast that the government will report the economy added 220,000 net new jobs in September

The service sector increased its payrolls by 160,000 in September, down from 155,000 in August, the new report said.