There have been 68 recent deaths of residents and nurses from the facility in a small New Jersey town.

The call for body bags came late Saturday.

By Monday, the police in a small New Jersey town had gotten an anonymous tip about a body being stored in a shed outside one of the state’s largest nursing homes.

When the police arrived, the corpse had been removed from the shed, but they discovered 17 bodies piled inside the nursing home in a small morgue intended to hold no more than four people.

“They were just overwhelmed by the amount of people who were expiring,” said Eric C. Danielson, the police chief in Andover, a small township in Sussex County, the state’s northernmost county.

The 17 were among 68 recent deaths linked to the long-term care facility, Andover Subacute and Rehabilitation Center I and II, including two nurses, officials said. Of those who died, 26 people had tested positive for the virus.

For the others, the cause of death is unknown.

Of the patients who remain at the homes, housed in two buildings, 76 have tested positive for the virus; 41 staff members, including an administrator, are sick with Covid-19, the disease caused by the coronavirus, according to county health records shared on Wednesday with a federal official.

Andover Subacute is not alone. The coronavirus has swept through the New York region’s nursing homes with devastating and deadly speed, killing thousands of residents at facilities struggling with staff shortages, increasingly sick patients and a lack of personal protective gear.

Staff members at the facility were asking the same thing.

“To all the people calling into the governor’s office, the congressman’s office to help us tell them WE NEED HELP,” a representative of Andover Subacute & Rehab Center Two wrote at 7:18 p.m. on Monday, in a Facebook post that was deleted on Wednesday.

After news began to be shared on Wednesday about the bodies found in the makeshift morgue, a discovery first reported by The New Jersey Herald, the fear intensified.

Mr. Gottheimer said his office had fielded calls from staff members and worried relatives pleading for help. He said he had spoken to a representative of the Federal Emergency Management Agency about the possibility of sending National Guard medics.

The state Department of Health sent two shipments containing 3,200 surgical masks, 1,400 N95 masks and 10,000 gloves to the nursing homes, said Donna Leusner, a spokeswoman. The first shipment went out about a week ago and the second should have been delivered Tuesday or Wednesday, she said.

“It’s scary for everybody — for the residents and for the staff,” Mr. Gottheimer said. “What is surprising to me is how many are dying in house, versus the hospital.”

The nursing home has told local health officials that they are housing sick patients on separate wings or floors, Chief Danielson said. And local residents have been gathering supplies to donate to the nursing home.

Several women created a Facebook page and a website, Sparta Helps Healthcare Heroes, to gather needed gowns, gloves and masks.

“At first, it was kind of like, ‘What can we do?’” said one of the organizers, LeeAnne Pitzer. “Now we have an army of sewers who are making handmade masks that can be washed and reused.”

One resident of Sparta, Cheryl Boggs, said she found three boxes of Tyvek suits and bootees in a storage room at the company where she works, Petro-Mechanics. She dropped them off on Monday after seeing the pleas for help on Facebook.

“We just wanted to help,” she said.

Lily Repasch, 84, died three weeks ago at Andover Subacute and Rehabilitation Center I.

Her son and three daughters were regular visitors to the facility, even talking through a window in her final days after the state ordered all long-term care facilities to stop allowing visitors.

The women said the facility offered no way for them to communicate with their mother, who had dementia, and provided family members no information. Their mother was never tested for the coronavirus.

“Her death was inevitable,” said one daughter, Lee Repasch. “But she was a vulnerable woman with dementia. It was inevitable, but it didn’t need to be like this.”

Most of the state’s nursing homes have reported at least one case of the coronavirus, which as of Wednesday had infected 6,815 patients of long-term care facilities in New Jersey. At least 45 of the 351 coronavirus-related deaths announced on Wednesday were residents of long-term care facilities.

Gov. Philip D. Murphy said that once the threat of the pandemic passes, New Jersey must take a hard look at what went wrong.

“It’s pretty clear that a big weakness in the system, and in reality, is long-term care facilities,” he said.

Thirteen of the bodies discovered on Monday at the Andover facility were moved to a refrigerated truck outside a hospital in nearby Newton, Chief Danielson said. A funeral home had made arrangements to pick up the other four.