The deaths at Peconic Landing included three men and three women, ages 88 to 97. The facility has not released the names of those who died. Family members were not permitted to be with some of the elders as they died, because of hospital restrictions to curb the spread of the virus.

Suffolk County, which includes some of the East Coast’s wealthiest beach communities, had 2,260 confirmed cases of Covid-19, and 20 deaths, as of Wednesday — at least one death in each of the last 7 days. “We’re seeing those numbers on a daily basis continue to rise,” Steve Bellone, the Democratic county executive, said. As elsewhere, there was a shortage of face masks, medical gowns, gloves and hand sanitizer.

Mr. Bellone said he has not been tested because of a shortage of tests.

Peconic Landing, which has 377 residents, or members, was seeking donations of protective gear for workers and residents, but a representative said that because of these donations, lack of equipment had not “impacted care” for any residents. Shortages of the essential protective equipment have been rampant at health facilities around the country, increasing risks of spread.

At a briefing for reporters, Robert J. Syron, president of Peconic Landing, was asked whether all residents and workers were being tested for the virus.

“We don’t have the ability,” he said, according to the local news site Patch. “We wish we could. There just aren’t enough tests. I have no control over it. If I could write a check to have every person tested, I would have written it.”

Peconic Landing has a five-star rating from the federal Centers for Medicare and Medicaid Services. The facility, where initial costs start at $247,000, plus monthly fees, occupies 144 acres by Long Island Sound, and ranges from independent-living cottages to skilled nursing and a memory care unit for people with dementia.

“Once it hit Long Island, we knew it would be here,” Mr. Syron told The Suffolk Times. “So we prepared well in advance. But we did not expect it would hit us like it did.”