WASHINGTON — Having wiped out the requirement for people to have health insurance, Republicans in Congress are taking aim at a new target: the mandate in the Affordable Care Act that employers offer coverage to employees.

And many employers are cheering the effort.

While large companies have long offered health benefits, many have chafed at the detailed requirements under the health law, including its reporting rules, which they see as onerous and expensive. Now that relief has been extended to individuals, some companies believe they should be next in line.

The individual mandate and the employer mandate are “inextricably entwined,” said James A. Klein, the president of the American Benefits Council, an influential lobby for large companies like Dow Chemical, Microsoft and BP, the oil and gas producer.

“It is inequitable to leave the employer mandate in place when its purpose — to support the individual mandate — no longer exists,” Mr. Klein said. “We are urging Congress to repeal the employer mandate.”