The law applies to companies with workers in New York City, but labor experts expect it to influence practices nationally. At least four states — California, New Jersey, New York and Vermont — and the District of Columbia are also working on laws to regulate A.I. in hiring. And Illinois and Maryland have enacted laws limiting the use of specific A.I. technologies, often for workplace surveillance and the screening of job candidates.

The New York City law emerged from a clash of sharply conflicting viewpoints. The City Council passed it during the final days of the administration of Mayor Bill de Blasio. Rounds of hearings and public comments, more than 100,000 words, came later — overseen by the city’s Department of Consumer and Worker Protection, the rule-making agency.

The result, some critics say, is overly sympathetic to business interests.

“What could have been a landmark law was watered down to lose effectiveness,” said Alexandra Givens, president of the Center for Democracy & Technology, a policy and civil rights organization.

That’s because the law defines an “automated employment decision tool” as technology used “to substantially assist or replace discretionary decision making,” she said. The rules adopted by the city appear to interpret that phrasing narrowly so that A.I. software will require an audit only if it is the lone or primary factor in a hiring decision or is used to overrule a human, Ms. Givens said.

That leaves out the main way the automated software is used, she said, with a hiring manager invariably making the final choice. The potential for A.I.-driven discrimination, she said, typically comes in screening hundreds or thousands of candidates down to a handful or in targeted online recruiting to generate a pool of candidates.