One child, 8 years old, arrived at a Long Island hospital near death last week. His brother, a boy scout, had begun performing chest compressions before the ambulance crew reached their home.

In the past two days alone, the hospital, Cohen Children’s Medical Center, has admitted five critically ill patients — ages 4 to 12 — with an unusual sickness that appears to be somehow linked to Covid-19, the disease caused by a coronavirus. In total, about 25 similarly ill children have been admitted there in recent weeks with symptoms ranging from reddened tongues to enlarged coronary arteries.

Since the coronavirus pandemic began, most infected children have not developed serious respiratory failure of the kind that has afflicted adults. But in recent weeks, a mysterious new syndrome has cropped up among children in Long Island, New York City and other hot spots around the country, in an indication that the risk to children may be greater than anticipated.

The number of children in the United States showing signs of this new syndrome — which first was detected in Europe last month — is still small. None is known to have died, and many have responded well to treatment.

No solid data yet exists about how many children in the United States have fallen ill with what doctors are calling “pediatric multisystem inflammatory syndrome.”

“This is really only a disease that has been clear for two weeks now, so there is so much we’re trying to learn about this,” the chief of pediatric critical care at Cohen Children’s, Dr. James Schneider, said in an interview on Tuesday.

Doctors say this condition does not seem to be driven by the virus attacking the lungs, a hallmark of coronavirus infection in adults.

While some of the children with this condition do end up with respiratory problems and a few have needed to be on ventilators, “it seems to be less a lung-specific disease,” said Dr. Steven Kernie, chief of pediatric critical care medicine at Columbia University and NewYork-Presbyterian Morgan Stanley Children’s Hospital, which has treated between 10 and 20 children with the condition, ranging from infants to older teenagers.

He said many of their symptoms — from rashes to redness of eyes to blood circulation problems — appear to be rooted in an “overall inflammatory response.”

In some patients the syndrome seems similar to a rare childhood illness called Kawasaki disease, which can lead to inflammation of the blood vessels, especially the coronary arteries.

The symptoms of Kawasaki disease often start with a fever and a rash, but when undiagnosed and untreated, the illness can lead to serious heart conditions, such as coronary aneurysms. The disease, which generally afflicts patients 6 months to about 6 years old, is considered rare in the United States.

But Dr. Kernie said it was important to distinguish between this coronavirus-related condition and Kawasaki disease.

While some of the symptoms are similar, Dr. Kernie said, including fever, abdominal pain and sometimes a raised rash, there appear to be differences in how the coronavirus-related condition affects the heart.

While shock is a rare complication of Kawasaki disease, in the recent wave of coronavirus-related cases, he said, many of the children are in toxic shock with very low blood pressure and an inability of the blood to effectively circulate oxygen and nutrients to the body’s organs.

On Monday night, the New York City Health Department issued a bulletin, asking doctors to report any cases of the syndrome. The bulletin said the health authorities in the city knew of 15 such cases, involving patients age 2 to 15, who have been in intensive care units since April 17.

But interviews with doctors in New York City and on Long Island suggest that at least 50 children have been treated for the syndrome, not all in intensive care.

“I would say so far we have seen 13 patients,” Dr. Nadine Choueiter of the Children’s Hospital at Montefiore in the Bronx said of the children treated for the syndrome at just her hospital.

Still, doctors were reluctant to speculate how widespread it might be across the city. “That is the question we are constantly thinking about, and I don’t think we know the answer,” Dr. Choueiter said.

In Richmond Hill, Queens, Jayden Hardowar, 8, initially had only a mild fever, starting on April 23, his father, Roup Hardowar, said.

But several days later, Jayden started to grow very weak and listless. On April 29, he was lying in bed watching a Pokemon TV episode. “Mommy,” he cried out, before he stopped breathing. His face started turning purple. His 15-year-old brother, a boy scout, began performing chest compressions, stopping only when the ambulance arrived, his father said.

At Cohen’s Hospital, in New Hyde Park, Jayden was put on a mechanical ventilator for three days before he began to improve. Although Jayden tested negative for the coronavirus, he tested positive for antibodies, suggesting he might have been infected with the virus in recent weeks or months, his father said.

In recent days, Jayden has begun to open his eyes and smile or cry at his parents during video chats arranged by a nurse. “Last night he said, ‘I love you, Mommy,’” his father recounted on Tuesday.

Jayden is one of 11 children in the intensive care unit at Cohen Children’s deemed to have the syndrome, doctors there said.

Similar cases have appeared elsewhere in the country, too.

Juliet Daly, a healthy 12-year-old from Covington, La., woke up on April 3 with such sharp pains in her stomach that she had trouble moving. “I spent one hour in bed trying, attempting to get up, and I spent half an hour going down the stairs,” Juliet said in an interview on Tuesday.

Over the weekend, she had a fever, and, she said, “I couldn’t eat and I couldn’t drink because I vomited everything up.” By Monday, “my arms were cold and my lips were blue,” she said.

She was so lethargic that “she kind of fell asleep in the bath,” said her father, Sean Daly.

The family took Juliet to a nearby hospital, where they were told that she was experiencing an acute form of heart inflammation called fulminant myocarditis. Her heart rate was very low, and her heart was failing to pump blood.

The hospital decided to put Juliet on a ventilator and airlifted her to a medical center in New Orleans, about 40 miles south. During the intubation procedure, her heart stopped, and “she went into arrest for a little under two minutes,” Mr. Daly said. Later, on the helicopter, her heart stopped again and she needed to be revived by C.P.R., he said.

After nine days in the hospital, she returned home to her parents and two brothers. “I was able to walk around, but I was still wobbly,” she said. Now, Juliet, who likes to bike and do artwork, is feeling healthy.

Doctors in New York have noted that cases of the new syndrome began to appear a month or so after a surge of Covid-19 in the region. That timing suggests “it’s a post-infectious immune response to this,” said Dr. Leonard Krilov, chairman of pediatrics at NYU Winthrop Hospital in Mineola, N.Y.

In some cases, the treatment for children with the new syndrome is straightforward and quick. Dr. Krilov recently treated a 4-year-old boy whose family had previously fallen ill with Covid-19. Weeks later, the boy had a high fever, a rash and kidney trouble. He was given one of the standard treatments for Kawasaki disease: intravenous immunoglobulin, a serum harvested from donated blood. Within a day his fever fell and kidneys returned to normal, Dr. Krilov said.

Early research suggests that children are significantly less likely to become seriously ill with Covid-19 than adults. In New York City there have been 13,724 deaths of laboratory-confirmed Covid patients. Six have been 17 years old or younger, and all had underlying health conditions, according to city data.

Doctors say that even though there is growing evidence that some healthy children are falling gravely ill with this new syndrome, they are still at far less risk from Covid-19 than adults.

“It’s just a different disease in adults,” said Dr. Jennifer Lighter, a pediatric infectious disease specialist at NYU Langone Medical Center, who treated one pediatric patient with the new syndrome last week.

“It is very, very rare, and the children have been doing OK for the most part,” Dr. Lighter said of the new syndrome. “My patient is home and doing great.”