Covid shots are a good option for children, but parents may not agree to them.

The Food and Drug Administration’s authorization of a Covid-19 vaccine for ages 5 to 11 on Friday makes 28 million unvaccinated children in the United States suddenly eligible for the shot and offers the country an opportunity to make big inroads in its efforts to achieve broad immunity against the coronavirus.

But in a nation that has already struggled mightily with Covid vaccine hesitancy, getting shots into those little arms may present health authorities with the toughest vaccination challenge yet.

Even many parents who are themselves vaccinated and approved the shot for their teenagers are churning over whether to give consent for their younger children, questioning if the risk of the unknowns of a brand-new vaccine is worth it when most coronavirus cases in youngsters are mild.

In announcing its authorization of a lower-dose shot made by Pfizer and BioNTech for the age group, the F.D.A. said clinical trial data showed the shot was safe and prompted strong immune responses in children. The most common side effects were fatigue, fever and headache.

Infectious disease experts say that with approaching holiday travel and family gatherings, widespread vaccination of younger children could be a game-changer: It could help keep classes in person, reduce the likelihood of quarantines and lessen the risk of transmission to older, vulnerable adults — as well as protect the children from what has become the eighth biggest killer in their age group, according to the Centers for Disease Control and Prevention. To date, nearly two million children age 5 to 11 have been infected with the virus and 8,300 have been hospitalized. A third of those hospitalized were admitted to intensive care units, and at least 170 have died.

But a report this month from researchers at Northeastern, Harvard, Rutgers and Northwestern Universities found that parental concerns around the Covid vaccination had increased “significantly” from June through September. Chief among them, researchers said, were the newness of the vaccine, whether it has been sufficiently tested, efficacy, side effects and long-term health consequences.

According to a survey released Thursday by Kaiser Family Foundation, scarcely one in three parents will permit their children in this newly eligible age group to be vaccinated immediately. Two-thirds were either reluctant or adamantly opposed. An Axios-Ipsos poll found that 42 percent of parents of these children said they were unlikely to have their children vaccinated.

Erin Gauch, of Middletown, R.I., got herself and her two older children, ages 14 and 12, vaccinated this summer. But she’s worried about the potential side effects of the shots for her son. One of those side effects is myocarditis, a weakening of the heart muscle, that has been reported in a very small number of teenage boys and young men after getting a Covid shot.

“I’m looking at a 9-year-old and if I make a bad decision and he ends up with some debilitating side effects or lifelong adverse reaction, I don’t think I could live with that,” she said.

This vaccine dilemma occurs at a turbulent cultural moment for parents of young children, who are often judged harshly on social media for their decisions. The choice can appear freighted with political affiliation. A decision can signify, intentionally or not, compassion or disregard for others and a willingness to follow or ignore advice from their pediatrician.

“If we ultimately decide not to get my youngest vaccinated right now, I guess I’ll be subjected to mommy shaming but I’ll just have to deal with it,” Ms. Gauch said.

Many parents, like Ms. Gauch, are focusing on some research that suggests the rare possibility that young men and boys will develop pericarditis, a weakening of the lining around the heart, and myocarditis, but the clinical trial data the F.D.A. reviewed showed no cases in the 5 to 11 age group. Many experts say that the conditions usually improve quickly and that Covid presents far greater risk of severe myocarditis.

The Biden administration recently announced that the shots would be given predominantly by pediatricians, community health centers and children’s hospitals, plus pharmacies and schools, which will carry the burden of persuading parents.

But a Kaiser policy brief noted that schools and pharmacists in regions where Covid vaccination rates are low may be reluctant to participate. Access in rural areas and for working parents will be considerable challenges, the authors said, and they noted that achieving equity will also be a concern: More than half of those newly eligible are children of color.

After what is expected to be an initial rush of eager parents (as happened with adults and teenagers), pediatricians say they are bracing for conversations they anticipate to be among the thorniest they have ever had.

“I know parents are probably bombarded with misinformation about vaccines, even within their social circles: ‘My friend said this, my mother-in-law said that,’” said Dr. Katherine Williamson, a pediatrician in Orange County, Calif. “I’m hoping I can make a difference.”

The decision is particularly hard for parents to make on behalf of their first child, said Emily Brunson, a medical anthropologist at Texas State University who researches parent vaccination choices. Because vaccine decision-making is so personal and complicated, she said, many parents are likely to put it off.

Vic Sandrin, who works for a bicycle company in Vancouver, Wash., supports vaccines but cautiously. He, his wife and their 18-year-old got the Covid vaccine grudgingly, to travel for work and family visits.

For his 11-year-old twins, however, he is content to wait: “I’m willing to take a chance on myself, and that made sense, I’m an adult,” Mr. Sandrin said. “But for kids who already have strong immune systems, I don’t know if there’s a reason to get them vaccinated, or at least not just quite yet. ”

At heart, the decision is about which unknown—Covid or the vaccine— that parents fear more. They may stack factors such as social routines, older relatives, school protocols and the likelihood of severe illness to confirm their intuitive bias about whether to allow their child to get the shot.

Ms. Gauch, a mechanical engineer, calculated each family member’s risk individually. She has asthma, so, for her, the vaccine was a no-brainer. Her 14-year-old daughter got her first job this summer; getting vaccinated meant she wouldn’t have to wear a face mask at work. And her 12-year-old daughter saw that getting vaccinated could open up possibilities of being maskless in public. Done and done.

But not only does Ms. Gauch worry about side effects in her 9-year-old son, she says that getting vaccinated won’t release him from following other Covid rules because his school insists on masks and social distancing. “He is much less likely to get Covid if they’re taking all these precautions,” she said. “So I just don’t see the risk payoff of the vaccine.”

Parents who were predisposed not to vaccinate their child tended to dismiss the threat of serious illness from Covid as minuscule, saying that children who became seriously ill most likely had underlying conditions.

The argument that vaccinating children contributes to the community’s overall health does not get much traction, either. Parents’ paramount focus is the well-being of their own child. Although health officials contend an important reason to vaccinate is to protect the child, some parents said they believed that their healthy children would be injected with a novel vaccine largely to safeguard older adults, who had already lived full lives.

In interviews, some parents said that if the vaccine gained full approval for children (as the adult dose has) and schools required it, they would consider withdrawing their students. Dr. Cynthia Bader, a pediatrician in the Seattle area with an 8-year-old son, said that if her school district issued a vaccine mandate, she would clap her hands with joy but “then cringe at the idea of all the parents who will be coming to me seeking counseling for vaccine exemption forms.”

Parents are siloing themselves with like-minded friends, which reinforces their thinking. “It used to be that more people with different opinions would mesh, but now I don’t think that is the case,” said Abby Cooper of Bergen County, N.J., who is eager to get her five children vaccinated.

But she has friends who refuse. “Their kids are going to school with my kids and putting them at risk for no reason. It’s very upsetting. So, sadly, I’ve lost friends over this.”

Many parents worry that the tension will infect the children themselves. Some foresee having to set boundaries about unvaccinated playmates, especially if exposure to the virus could jeopardize someone else in the home.

Many parents will be difficult to persuade. The C.D.C. and the American Academy of Pediatrics have published talking points for pediatricians and other proponents of the Covid vaccine for children.

Consensus: First, address the parents’ questions. But if they don’t want to hear The Talk, don’t force it.

Consensus: Fear tactics — generalized descriptions of children suffering in Covid wards — don’t work.

Consensus: Emphasize the benefits of the Covid vaccine to the child in terms of emotional and physical well-being, including some semblance of pre-Covid social life. Invoke quarantines, remote learning.

Kim Cobb hopes that her family’s Covid ordeals will show others the benefits of vaccinating all eligible family members. She, her husband and their two older daughters, 14 and 12, got vaccinated quickly. But in August, her unvaccinated 10-year-old twins came down with Covid. Soon after, Dr. Cobb, a climate scientist at Georgia Tech, and her husband tested positive for breakthrough infections. Their two vaccinated children remained healthy.

The parents became miserably ill but did not require hospitalization, which they believe is because they were vaccinated.

All recovered, but Dr. Cobb and one twin have lingering respiratory distress.

“We’re in the third month post-infection and we have to see pulmonologists, we have inhalers, we’re on medication and we’re still having breathing difficulties,” Dr. Cobb said. “And this is not a kid who ever had respiratory symptoms.”

“It was not foreseeable,” she continued. “If you could avoid it, you would.”