Covid-19 vaccinations for children 5 to 11 years old are off to a slow start in many parts of the U.S., federal data show, underscoring the challenges health officials face in persuading parents to inoculate their children.

Roughly five million, or 18%, of the estimated 28.4 million U.S. children in the 5-to-11 age bracket have gotten at least one shot in the five weeks since they were cleared to get vaccinated, the data show. The picture varies by region, with rates in several New England states above 30% and some states...

Covid-19 vaccinations for children 5 to 11 years old are off to a slow start in many parts of the U.S., federal data show, underscoring the challenges health officials face in persuading parents to inoculate their children.

Roughly five million, or 18%, of the estimated 28.4 million U.S. children in the 5-to-11 age bracket have gotten at least one shot in the five weeks since they were cleared to get vaccinated, the data show. The picture varies by region, with rates in several New England states above 30% and some states in the South far off the national pace, an analysis by The Wall Street Journal of the data shows.

About three in 10 parents reported they had gotten their 5- to 11-year-olds a shot or said they planned to right away, according to polling of parents’ views from the Kaiser Family Foundation released Thursday, while 32% said they were going to wait and see, 7% said they would only if required and 29% said they definitely wouldn’t.

A health worker administered a Covid-19 test Tuesday on a child outside a pharmacy in Providence, R.I.

Photo: David Goldman/Associated Press

Other analysis from the foundation, published Wednesday, found the pace of vaccinations for 5- to 11-year-olds nationally had slowed significantly after initial high demand. Health authorities in some slower-moving states said they thought they could still get most parents on board, though it may take time.

“The biggest challenge we have here, which is probably across broader Appalachia as well, is the messaging has to come from a trusted medical provider or a trusted individual in the family,” said James Hoyer, who leads the Joint Interagency Task Force for Covid-19 in West Virginia.

“So it’s going to be a much longer lead time for us to get people comfortable,” he said.

State data recently showed about 15,300, or 11%, of the 140,000 children aged 5 to 11 in West Virginia have gotten at least one shot.

Vermont leads the U.S. with at least 47% of its children in the 5-to-11 bracket having received a shot, the Journal analysis of the federal data shows. Vermont, where nearly 84% of adults are fully vaccinated, has long been a fast adopter of Covid-19 vaccines. Massachusetts, Maine and Rhode Island also are high on the list for young children, as they are with adults. Alabama, Louisiana and Mississippi have started slowly with children in the 5-to-11 age group, echoing the South’s broader vaccine-uptake trends.

Children aged 5 to 11 started getting their first doses of Covid-19 vaccines on Nov. 3, after the CDC recommended use of the Pfizer-BioNTech shot for that age group. Some parents said they were eager for kids to get vaccinated and return to normal life. Photo: Maddie McGarvey/WSJ The Wall Street Journal Interactive Edition

State vaccination data and Centers for Disease Control and Prevention data may differ in some cases, in part because of reporting lags.

Most infectious-disease experts have encouraged vaccines for children. While they typically experience milder cases than adults if they get Covid-19, children can and do get sick from it. They are also a part of the puzzle when it comes to achieving broad, communitywide protection.

Researchers haven’t found evidence the vaccines pose additional or different risks to children than to adults. Parents still often approach the shots cautiously, some pediatricians said. The new poll found safety and potential side effects were prominent concerns among parents.

“The younger a child is, the more a family tends to want to sit down with a medical professional they trust and talk through their questions,” said Lee Beers, president of the American Academy of Pediatrics.

Covid-19 can cause heart-inflammation conditions. The conditions have also been reported in a smaller number of people who got an mRNA vaccine, most commonly in male adolescents and young adults.

The new Kaiser Family Foundation poll, of roughly 1,200 parents with a child under 18, was conducted between Nov. 8 and Nov. 23, before the Omicron variant hit the news, and included. The margin of error is 4 percentage points for the full sample and 5 points for parents with children in the 5-to-11 group.

Vaccine acceptance continues to break along political lines. About half of polled parents who self-identified as Republican said they wouldn’t vaccinate eligible children, compared with 7% of parents who self-identified as Democrats. Among self-identified independents, 33% said they wouldn’t vaccinate children aged 12 to 17 and 26% said they wouldn’t vaccinate those 5 to 11.

The polling also shows vaccine uptake among adolescents aged 12 to 17 has slowed after an initial surge. Parents of children in the 5-to-11 group seem less eager than parents of adolescents, according to the poll.

A family with young children signed up Tuesday for booster shots and vaccinations in Stamford, Conn.

Photo: Amir Hamja for The Wall Street Journal

Louisiana recently reported that about 7% of its 5- to 11-year-olds had gotten at least one vaccine shot. The full vaccination rate for all Louisianans, about 49%, also lags behind the nation’s 60% level, federal data show.

Kimberly Hood, assistant secretary of public health in Louisiana’s Department of Health, said she thought most parents could be persuaded, and that health authorities were trying to make inroads where they could. A recent clinic at a Baton Rouge arcade delivered about 480 new vaccine shots.

“We do feel there’s that movable middle that just wants information,” Ms. Hood said.

—Paul Overberg contributed to this article.

Write to Jon Kamp at jon.kamp@wsj.com