Moderna Inc.’s Covid-19 vaccine safely induced robust immune responses in children ages 6 months to 5 years in a new study, the company said, though the shot had modest efficacy against the Omicron variant.

Moderna said Wednesday the vaccine’s efficacy against symptomatic infections was 43.7% in children ages 6 months to 2 years, and 37.5% in children ages 2 to 5.

The efficacy rates were lower than seen during adult testing, which took place before Omicron emerged, but comparable to the real-world effectiveness of two doses of Moderna’s vaccine found among adults during the Omicron wave.

The Cambridge, Mass., company said it will seek regulatory authorization of its shot for young children in the U.S., Europe and other countries in the coming weeks.

If regulators agree, one of the last remaining age groups not eligible for Covid-19 vaccination in the U.S.—children under 5 years—could finally begin to receive the shots.

The vaccine from Pfizer Inc. and its partner BioNTech SE is authorized for anyone 5 years and older, while Moderna’s has only been available to adults 18 years and older in the U.S. to date.

“We believe these results are really good news for the parents of children who are under 6 years of age, and for the children themselves,” Jacqueline Miller, senior vice president of infectious diseases at Moderna, said in an interview. “We are hopeful to be able to bring this vaccine forward to address that unmet medical need.”

The request for clearance in young children is part of Moderna’s broader plans to expand use of the vaccine.

The company said it has initiated a request to the FDA to authorize use of its vaccine in children 6 to 11 years. The company previously said its vaccine safely induced immune responses in this age group.

Moderna also said it has provided the FDA with new information on use of its vaccine in adolescents 12 to 17 years.

Moderna last year applied for FDA clearance for this age group after a study showed the vaccine induced immune responses in the group. But the FDA delayed a decision because it wanted to review the potential risk of heart-inflammation conditions, including myocarditis. Moderna is providing longer-term safety data to the FDA, Dr. Miller said.

Efforts to widen the Covid-19 vaccination campaign to include children under 5 years have hit setbacks, frustrating some parents who want their young kids vaccinated. Some parents, however, have no intention of getting their younger children vaccinated. A Kaiser Family Foundation poll in January found that 26% of parents with children under 5 said they would definitely not get their kids vaccinated.

The FDA last month delayed a decision on the use of the Pfizer-BioNTech vaccine in children under 5 years after the companies got mixed results in clinical testing.

Two doses of the Pfizer-BioNTech vaccine didn’t produce a strong immune response in 2- to 4-year-olds, but did so in children under 2 years. The companies are waiting for additional results to see whether providing a third dose improves the immune response.

The risk of severe Covid-19 is much lower in children than in older adults, but there is still some risk. Covid-related hospitalization rates for children in the U.S. rose sharply during the winter surge of Covid-19 cases caused by the Omicron variant, according to the Centers for Disease Control and Prevention.

The results of the Moderna pediatric trial are encouraging, said Tina Tan, professor of pediatrics at Northwestern University Feinberg School of Medicine and infectious-disease specialist at the Ann & Robert H. Lurie Children’s Hospital of Chicago. Dr. Tan said a vaccine is needed for younger children, and it would be a better option for kids to take two doses for primary vaccination, rather than the potential for three doses if that turns out to be needed for the Pfizer vaccine.

Last year, Moderna, in collaboration with federal agencies including the National Institutes of Health, started a trial of its vaccine in children as young as 6 months up to 11 years, and eventually enrolled about 11,700 in the U.S. and Canada.

The trial included about 4,200 children ages 2 to 6 years, and about 2,500 children ages 6 months to under 2 years. Some were given two doses of the vaccine while others were given placebos, four weeks apart.

The dosage for children who got the vaccine was one-fourth the amount used for adults.

In the study, the vaccine induced comparable levels of neutralizing antibodies against the coronavirus in the young children as were seen in adults 18 to 25 years in a separate study conducted in 2020, Moderna said.

The vaccine’s efficacy against symptomatic disease, however, was more modest in children than was seen in the adult trial. Moderna’s full-dose vaccine was 94.1% effective against symptomatic Covid-19 in the adult study.

Moderna said the Omicron variant of the coronavirus predominated in the U.S. during the study of children under 6 years, and the company attributed the different results to Omicron, which began spreading late last year.

Moderna said real-world data has shown the vaccine’s efficacy for adults was reduced during the Omicron surge.

Moderna said the majority of confirmed Covid-19 cases in the pediatric trial were mild, with no severe cases or those resulting in hospitalization or death.

Dr. Miller said the lower dose used for children struck a balance between inducing a sufficient immune response and maintaining an acceptable safety profile.

Most side effects, like injection-site pain and fever, were mild or moderate, Moderna said. The company observed no new safety concerns, and there were no deaths, myocarditis or cases of an inflammatory syndrome in children reported in the study, Moderna said.

Moderna also plans to test the potential of a booster dose for all child populations.

Write to Peter Loftus at peter.loftus@wsj.com