Los Angeles requires proof of vaccination to enter many businesses, one of the nation’s strictest rules.

Los Angeles will require most people to provide proof of full coronavirus vaccination to enter a range of indoor businesses, including restaurants, gyms, museums, movie theaters and salons, in one of the nation’s strictest vaccine rules.

The new law, which was approved by the Los Angeles City Council on Wednesday, will allow people with medical conditions that do not allow them to be vaccinated, or who have a sincerely held religious objection, to instead show proof of a negative coronavirus test taken within the preceding 72 hours.

It will take effect on Nov. 4, which city officials have said should give the city and businesses enough time to figure out how the rule should be enforced.

Some council members have expressed concern that businesses would be unfairly burdened by the requirement, and that the city’s law is inconsistent with Los Angeles County rules that apply to neighboring communities and require masks indoors, but not proof of vaccination.

Still, city leaders said at a lengthy discussion of the measure last week that they wanted to move with urgency.

“We can’t let the perfect be the enemy of the good,” Kevin de León, a council member, said at the previous meeting.

A growing number of bars and restaurants are, on their own, already checking vaccination status. And mounting evidence suggests that employer vaccination mandates have been effective in boosting immunization rates.

In California, requirements that health care workers be vaccinated have helped increase vaccination rates at major health systems to 90 percent or higher. Major corporations have said their requirements have resulted in surging vaccination rates.

Implementing rules that require people to prove their vaccination status has been complex. A number of competing electronic “vaccine passports” are available, but some people need paper verification.

In August, New York became the first city in the nation to require proof that workers and customers at indoor sites for dining, physical fitness and entertainment had received at least one dose of a vaccine.

Not long after, some cities and counties in California, including San Francisco, followed suit. The addition of Los Angeles — by far the largest city in the state, with 4 million people — significantly alters the balance.

California’s elected leaders — especially Gov. Gavin Newsom — have highlighted pandemic restrictions across the state to draw a contrast with other states, where rules are more lax and cases among unvaccinated people have strained hospitals. California has one of the lowest case rates in the nation, and 70 percent of residents age 12 and older are fully vaccinated.

Last week, Mr. Newsom announced the nation’s first requirement that schoolchildren be vaccinated, starting as soon as next fall.