Alan Chvotkin, executive vice president for the Professional Services Council, a trade association that represents federal contractors, hailed the measure, which Mr. Trump may now sign into law. He said the rule was onerous and unfair, because companies had to report unproved accusations.

“The regulatory scheme was overly burdensome,” Mr. Chvotkin said. “We applaud the change.”

As an agency, OSHA has long struggled to have an impact. Its rule-making procedures are arduous, and changes can take years or even decades to enact.

Last year, to help the agency flex its muscles, Congress passed a law doubling the fines companies faced for safety violations. The agency also took aim at certain industries it considered repeat offenders.

Among other things, it levied fines last year as high as $317,000 against several poultry producers like Tyson Foods, Koch Foods and Birdsboro Kosher Farms. It also assessed a $2.5 million fine against Ajin USA, a company in Alabama that supplies auto parts for South Korean carmakers like Kia and Hyundai, after a 20-year-old woman was killed when a factory robot malfunctioned.

Still, the Trump administration and lawmakers seem to be making good on commitments to roll back regulations on businesses, and OSHA appears to be a prime target.

Industry groups are pushing back against an Obama-era regulation meant to exert pressure on companies to better comply with record-keeping rules. A provision of that rule, which was supposed to take effect last month, would require companies to electronically submit accident data to OSHA so the agency could post the information on a public website. As recently as early January, OSHA said on its website that it expected the site to be live in February.

But in recent weeks, the agency changed the wording so that it now states, “OSHA is not accepting electronic submissions at this time.”