Despite the reopening of most private museums in Washington, the Smithsonian and the National Gallery of Art have no set date to reopen from pandemic-related closures that began in November.

“Like everyone, I want to open as quickly as I can. For me, it’s the spring,” Smithsonian Secretary Lonnie G. Bunch III said Tuesday. “If we can open in May, that would be great. It might be early June.”

His top priority is the safety of staff and visitors, Bunch said. “We are always looking at the numbers, and they are rising a little bit,” he said.

The Smithsonian closed its buildings in November as cases began to spike in the region. When they are ready to reopen this spring, they will mimic last summer’s multiphased approach, Bunch said, with the National Zoo one of the first to come back. The phased reopening will be faster than last time, when it took two months to open eight sites.

“We won’t need as much time,” he said. “Every Friday, we could do a few more.”

The National Gallery of Art also predicts a spring opening of both its West and East buildings, according to Director Kaywin Feldman. The West Building reopened for several months last year, while the East Building remained closed for construction. The gallery’s outdoor sculpture garden, and the Smithsonian gardens, are open.

“We don’t want to reopen and reclose again,” Feldman said Tuesday. “We are watching lots of data. We are being very cautious. As I said all along, the top priority is the health and safety of our visitors and staff.”

The museum is taking its cues from the Biden administration, which is sounding the alarm about a potential fourth wave of cases, Feldman said. Nationally, coronavirus cases have increased 13 percent, with the seven-day average of new cases exceeding 63,000 for the first time in nearly a month, according to Washington Post data. The city’s cases have increased, too.

“That caution is directing our considerations,” Feldman said.

Meanwhile, Planet Word, Glenstone and the National Building Museum have announced plans to bring visitors back over the next week. They join the already-open Museum of the Bible, the International Spy Museum, the National Museum of Women in the Arts and the Phillips Collection.

Planet Word reopens Thursday on a reduced schedule, a decision that is based on the region’s health data and the return of many community organizations, said Executive Director Patty Isacson Sabee.

“The whole community is moving forward to open up,” Sabee said. “As more people are vaccinated, there’s a sense of optimism. It’s spring break, and people are having the ability to get out and experience things more.”

Like the other sites, Planet Word will limit capacity and require masks and social distancing. With just 200 guests admitted between 10 a.m. and 5 p.m., Sabee said, “we will be able to maintain a safe way to experience the museum.”

The National Building Museum will be open Friday through Sunday starting April 9. Tickets will be available for two sessions a day, from 11 a.m. to 1 p.m. and 1 to 4 p.m. Glenstone opened its outdoor spaces March 4 and will reopen its indoor galleries April 8 with a new Faith Ringgold exhibition.

The Phillips Collection opened in early March with a museum-wide centennial celebration, “Seeing Differently.” Director and chief executive Dorothy Kosinski said the reopening has been a balm to both her staff and visitors.

“We all have such pent-up emotions,” Kosinski said. “To be able to go into a museum, where you feel welcome and safe and there is beautiful art, provocative art, new art and old friends. You can feed your spirit and soul. Maybe now more than ever we all realize how critical and central art is to our lives.”

The reopening of the city’s museums is also critical to Washington’s comeback, said Elliott Ferguson, president and chief executive of Destination DC, a nonprofit supporting Washington tourism. But the Smithsonian is the most important.

“It is extremely important that those museums are open, but the perception is still tied to what happens with the Smithsonians,” Ferguson said. “We are extremely excited about those that are open. We want the zoo and the other Smithsonians to open.”

Feldman, the National Gallery’s director, said the experience gained from the summer and fall will make a spring reopening easier.

“Within about two weeks, we’ll be able to organize and have everything in place,” Feldman said, referring to timed tickets and such safety protocols as masking, social distancing and managing traffic flow.

“Everyone is eager to come back, eager to experience art and that togetherness and a sense of normalcy,” she said. “I had hoped [to reopen] mid-March, and that didn’t happen. I do believe it’s getting really close.”