US private-sector employment rose by 154,000 jobs in September from August, according to the ADP national employment report.

“The current record of consecutive monthly job gains continued in September,” said Mark Zandi, chief economist of Moody’s Analytics. “With job openings at all-time highs and layoffs near all-time lows, the job market remains in full-swing. Job growth has moderated in recent months, but only because the economy is finally returning to full employment.”

The number of goods-producing jobs rose by 3,000, following July losses of 9,000. Service-providing jobs rose by 151,000.

Large businesses added 64,000 jobs, down from the 67,000 added in August. Midsize businesses added 56,000 jobs in September, up from last month’s gain of 40,000.

Small businesses added 34,000 jobs in September, down from 68,000 in August.

Bloomberg reports companies added the fewest workers in five months, showing the labor market is cooling after strong gains for much of this year. Hiring managers might be having some trouble finding skilled workers to fill vacancies, helping explain the cooling in payroll gains even as the labor market remains healthy. Unless job figures released Friday by the Labor Department are a major disappointment, a measured slowdown would probably affirm Federal Reserve officials’ projections and keep them on pace to raise the benchmark interest rate before year’s end, according to Bloomberg.

The ADP National Employment report is produced by ADP (NASD: ADP) in collaboration with Moody’s Analytics.