Plays, concerts and other performances can resume in New York starting next month — but with sharply reduced capacity limits — Gov. Andrew M. Cuomo said Wednesday.

Mr. Cuomo, speaking at a news conference in Albany, said that arts, entertainment and events venues can reopen April 2 at 33 percent capacity, with a limit of 100 people indoors or 200 people outdoors, and a requirement that all attendees wear masks and be socially distanced. Those limits would be increased — to 150 people indoors or 500 people outdoors — if all attendees test negative before entering.

A handful of venues immediately said they would begin holding live performances, which, with a handful of exceptions, have not taken place in New York since Broadway shut down last March 12.

The producers Scott Rudin and Jane Rosenthal said they expected some of the earliest performances would take place with pop-up programs inside Broadway theaters, as well as with programming at nonprofit venues that have flexible spaces, including the Apollo Theater, the Park Avenue Armory, St. Ann’s Warehouse, the Shed, Harlem Stage, La MaMa and the National Black Theater.

“That communion of audience and performer, which we’ve craved for a year, we can finally realize,” said Alex Poots, the artistic director and chief executive of the Shed, which plans to begin indoor performances for limited-capacity audiences in early April.

The new rules will not affect commercial productions of Broadway plays and musicals, which are still most likely to open after Labor Day, according to Charlotte St. Martin, the president of the Broadway League.

“For a traditional Broadway show, the financial model just doesn’t work,” she said. “How do we know that? Because shows that get that kind of attendance close.”

Mr. Cuomo announced his plan to ease restrictions as New York, along with New Jersey, has been adding new coronavirus cases at the highest rates in the country over the last week: both reported 38 new cases per 100,000 people. (The nation as a whole is averaging 20 per 100,000 people.) And New York City is currently adding cases at a per capita rate roughly three times higher than that of Los Angeles County.

The labor union Actors’ Equity responded by calling on Mr. Cuomo to “prioritize getting members of the arts sector vaccinated.”

Many nonprofit leaders welcomed the new rules as a sign of hope and a first step toward recovery. “We have suffered immense loss and there’s a way to go,” said Oskar Eustis, the artistic director of the Public Theater, “but this policy change signals that we are turning a corner on the worst crisis the American theater has ever experienced.”

Lincoln Center and the Glimmerglass Festival have already announced plans to perform outdoors this year, and the new rules clarify how many people can attend.

“We welcome the new guidelines and want to serve as many people on our campus as is safe,” said Isabel Sinistore, a spokeswoman for Lincoln Center, which is planning to open 10 outdoor performance and rehearsal spaces on April 7.

For many New York music venues, operating at 33 percent capacity still may not be enough to make reopening economically feasible, give the costs of running the venues and paying performers.

“It doesn’t make financial sense for the Blue Note to open with only 66 seats for shows,” said Steven Bensusan, the president of the Blue Note Entertainment Group, whose flagship jazz club is in Greenwich Village.

Smaller music venues, which are among the eligible recipients of $15 billion in federal aid, have been anxiously awaiting permission to reopen. But even with growing vaccination numbers and New York’s latest rule change, it may still take months for the touring industry to resume, and even then venues say they will need help.

The Blue Note, along with some other jazz spots that serve food, had reopened last fall for dinner performances, allowing them to put on some shows without running afoul of state regulations that had banned anything but “incidental” music. (Some venues, and musicians, had filed lawsuits challenging those rules.) Then the city shut down indoor dining again, and some clubs did not reopen when it was allowed to resume last month.

Michael Swier, the owner of the Bowery Ballroom and Mercury Lounge, two of New York’s best-known rock clubs, said that the state’s order that venues require social distancing and mask-wearing means that the true capacity at many spaces may be much lower.

“Given that social distancing is still part of the metric, it brings us back down to an approximate 20 percent capacity, which is untenable,” Mr. Swier said.

Several promoters and venue operators said they were holding out to reopen at 100 percent capacity, which many hope can happen this summer.

But some small nonprofits immediately expressed interest. At the Tank, a Midtown Manhattan arts venue with a 98-seat theater, Meghan Finn, its artistic director, said that within hours of the governor’s announcement she started hearing from comedians eager to resume indoor performance.

“Having the ability to use our space is not something we will pass up,” Ms. Finn said.

The Joyce Theater in Manhattan had been expecting to bring audiences back to see live dance in September, but Linda Shelton, its executive director, said that she and her team had “hard work” to do in the coming days, as they assess whether staging a performance in the near term makes financial sense and can be done safely.

“We’ve got a few things that we could present pretty quickly,” she said.

Leon Botstein, the president of Bard College, home to the Fisher Center for the Performing Arts in Annandale-on-Hudson, the site of a respected music festival each summer, called the moves a “welcome first step.”

“One hundred is a good beginning number,” Mr. Botstein said. “That’s April’s number. Let’s hope June’s number is larger.”

A variety of nonprofit theaters said they found the news encouraging.

Paige Evans, the artistic director of Signature Theater, said that she had already commissioned the playwright Lynn Nottage and the director Miranda Haymon to create a multimedia performance installation in the theater’s capacious lobby this summer, and that the new rules should allow for audiences to attend.

Rebecca Robertson, the founding president and executive producer of the Park Avenue Armory, said she, too, is eager to welcome people back. “To have live audiences responding to the work is going to be thrilling,” she said.

Other organizations said the relaxed rules would allow them to imagine new programming. El Museo del Barrio said it would seek to develop outdoor work for parks, on streets, or in borrowed spaces.

“Finally,” said Leonard Jacobs, interim executive director of the Jamaica Center for Arts & Learning in southeast Queens, “we have good guidance from the state to help us take the first steps back to normal life.”

Ben Sisario and Matt Stevens contributed reporting.