WASHINGTON, Oct 5 (Reuters) - U.S. private employers stepped up hiring in September, suggesting demand for workers remains strong despite rising interest rates and tighter financial conditions.

Private employment rose by 208,000 jobs last month, the ADP National Employment report showed on Wednesday. Data for August was revised higher to show 185,000 jobs created instead of 132,000 as previously reported. Economists polled by Reuters had forecast an increase of 200,000 private jobs.

The ADP report resumed publishing in September, with the August data, after a two month hiatus as the company sought to improve the methodology for the data following a poor record predicting the private payrolls count in the Labor Department's Bureau of Labor Statistics employment report.

The jury is still out on whether the new ADP report, now jointly developed with the Stanford Digital Economy Lab, will be a useful labor market guide.

The report was published ahead of the BLS' more comprehensive and closely watched employment report for September.

According to a Reuters survey of economists, private payrolls likely increased by 270,000 jobs last month after rising by 308,000 in August. With the government sector expected to shed 20,000 jobs, that would lower overall nonfarm payrolls gains to 250,000. The economy created 315,000 jobs in August.

Job growth is slowing as employers adjust to cooling demand caused by stiff interest rate increases from the Federal Reserve, which is wrestling high inflation.

The government reported on Tuesday that job openings dropped by 1.1 million, the largest decline since April 2020, to 10.1 million on the last day of August. (Reporting by Lucia Mutikani; Editing by Chizu Nomiyama)