Gyms in New York, which have remained shuttered for months even as the state made progress in fighting the coronavirus, will be allowed to open again as soon as Aug. 24 and no later than Sept. 2, Gov. Andrew M. Cuomo said on Monday.

Mr. Cuomo’s announcement came with several caveats: Gyms would be limited to a third of their total capacity, and people would be required to wear masks at all times. The state would also require a sign-in form to assist with contact-tracing efforts.

Local governments will also need to inspect gyms to make sure they meet the state’s requirements before they open or within two weeks of their opening. Local governments can stop gyms from holding indoor classes, Mr. Cuomo said.

The decision marked a significant step forward in the state’s return to the pre-pandemic status quo, even as officials have grown concerned about a second wave of the virus.

Gyms and fitness centers have been closed in New York City since March 16, and statewide since March 22. Even though the entire state had moved into the fourth and final stage of Mr. Cuomo’s reopening plan by mid-July, officials ordered gyms to remain shut over concerns that the virus could spread more easily in them.

“We know gyms are highly problematic from the other states,” Mr. Cuomo said earlier this month, as cases rose across the country and New York continued to keep its outbreak under control.

Health experts have worried that intense indoor exercise could pose significant risks, both from activity that produces higher concentrations of the virus and from equipment that is touched frequently. Health clubs in New Mexico and California have been linked to a small number of virus cases.

Epidemiologists have also said that they believe the risk of transmission is higher indoors, which led Mr. Cuomo in June to keep gyms, as well as movie theaters, shopping malls and bowling alleys, closed.

Similar concerns also led state officials to delay allowing indoor dining in dense and crowded New York City, even as they allowed it elsewhere in the state.

Though some businesses and trainers have tried to adapt to regulations by moving classes or sessions outside, struggling gym owners have been frustrated by the state’s decision for weeks. More than 1,500 of them joined a class-action lawsuit filed last week that aimed to force New York to allow their reopening. A hearing is scheduled in the case for Thursday, according to court records.

The NYS Fitness Alliance, an industry group that represents more than 2,700 facilities statewide, had submitted reopening recommendations to the governor’s office that called for reopening gyms at 50 percent capacity and requiring masks only when people were not exercising, as some states have done.

Mr. Cuomo said the state’s guidelines were created after discussions with health officials and after researching reopening guidelines in the rest of the country.

“We’re prepared to enforce whatever protocol they roll out,” said Bill Lia, the chair of the NYS Fitness Alliance and owner of four gyms in the Albany area. “We’re excited to get our employees back to work and start getting back to helping our members.”

Mr. Lia said that managing capacity would not be a large hurdle, since most gyms already require customers to check in. Some national gym chains that have locations in New York have elsewhere required gymgoers to make appointments.

Mr. Lia said it was unclear how many gyms have permanently closed in New York because of the pandemic. But he noted that smaller, independent facilities were disproportionately affected by the restrictions compared with bigger operators that might have better absorbed losses.

“There is definitely going to be some fallout in the industry,” he said.

Gyms have also been closed in New Jersey, except for private personal training sessions, though Gov. Philip D. Murphy said on Friday that officials were discussing whether and when they would be able to reopen. Connecticut allowed fitness centers to reopen, with limits, in June.

At least 43 states and Washington, D.C., have allowed gyms to reopen in some or all parts of the state, according to the International Health, Racquet & Sportsclub Association, a nonprofit trade group.

Mr. Cuomo said on Monday that gyms would be allowed to reopen because New York has successfully kept its rate of positive coronavirus test rates hovering around 1 percent since June.

Still, Mr. Cuomo said that he remained worried that reopening gyms might accelerate the virus’s spread. He said his main concern was that local governments would not adequately enforce the state’s restrictions, noting, as he has before, how many cities and towns have not aggressively cracked down on bars and restaurants ignoring social distancing measures.

It was not immediately clear when New York City would clear gyms for reopening, or which agency would be responsible for conducting inspections or enforcing regulations.

Mitch Schwartz, a spokesman for Mayor Bill de Blasio, said that the city would develop its inspection system in the coming weeks, but that it did not plan to initially allow indoor fitness classes when gyms reopened.

In addition to gyms, the state has kept movie theaters, casinos and amusement parks shuttered. Mr. Cuomo did not say when he believed those businesses could reopen, but said that officials were continuing to evaluate the risks involved.

“We’re saying today that gyms for New Yorkers are more essential than movie theaters,” Mr. Cuomo said on Monday.

Last week, Mr. Cuomo announced that museums and other cultural institutions in New York City, which stayed closed even as their counterparts reopened in the rest of state, would be allowed to reopen on Aug. 24, at 25 percent capacity and with timed ticketing.

Also last week, Mr. Cuomo gave bowling alleys statewide the green light to reopen with strict protocols in place: Every other lane is supposed to be blocked off because of social distancing, and bowling equipment must be properly sanitized.

The loosening of restrictions comes as the city has managed to sustain low rates of infections for weeks, surprising even top officials. As of Monday, the infection rate statewide has hovered below 1 percent for the past 10 days.

Nevertheless, state and city officials have been bracing for a potential second wave, growing increasingly concerned about New Yorkers becoming complacent with social distancing and about out-of-state travelers spreading the virus. Travelers from more than 30 states, plus Puerto Rico and the U.S. Virgin Islands, are required to quarantine for 14 days upon arrival in New York.

But epidemiologists fear that the travel restrictions may not be enough to hold off the virus, and that the reopening of more indoor settings may provide additional ground for it to spread.

Tracey Tully contributed reporting.