WASHINGTON — U.S. companies added a modest 135,000 jobs in September, a private survey found, a sign that hiring is slowing as the trade war takes a toll on the economy and employers grow cautious.

Payroll processor ADP said Wednesday that hiring has particularly slowed in mining, which actually cut 3,000 jobs, and manufacturing, which added just 2,000. Health care providers added 35,000 jobs, while a category that mostly includes hotels and restaurants reported 18,000 more jobs.

Job gains at last month’s pace are enough to keep the unemployment rate from rising. And there are few signs of widespread layoffs. But companies’ demand for labor, which pushed average monthly hiring to 225,000 last year, has waned in the past six months.

President Donald Trump has slapped tariffs on more than half of Chinese imports and has also placed duties on steel, aluminum, and washing machines. China and other countries have imposed retaliatory tariffs, including on agricultural products including soybeans, which have clobbered farmers and imposed further pain on manufacturers.

Mark Zandi, chief economist at Moody’s Analytics, which compiles the ADP data, said that about one-fifth of the U.S. economy — manufacturing, farming and transportation — is essentially in recession. Shippers have fewer crops and manufactured goods to transport.

“The trade war is doing real damage to the economy,” he said.

Large companies, with more than 500 employees, continued to outpace other firms, adding 67,000 jobs, ADP said. Small companies with fewer than 50 workers gained just 30,000. Medium-sized firms added 39,000.

The ADP’s figures don’t include government hiring and frequently diverge from the government’s official report, which is scheduled to be released Friday. Economists expect that report will show 140,000 jobs were added.

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