WASHINGTON — U.S. businesses added 213,000 jobs in September, stepping up hiring for the sixth straight month, according to a private survey.

Payroll processer ADP said the pace of hiring by private employers was up slightly from 202,000 in August. Job gains above 200,000 are usually enough to cut the jobless rate.

The figures suggest the government’s jobs report on Friday could reveal a rebound in hiring. The government said employers added only 142,000 jobs in August. But the ADP numbers cover only private businesses and sometimes diverge from the government’s more comprehensive report. ADP’s August figure was much higher than the government’s.

Economists forecast that the government’s report will show 215,000 jobs added in September.