However the F.D.A. rules, Michelle Goebel, 36, of Carlsbad, Calif., said she is nowhere near ready to vaccinate her children, who are 8, 6 and 3, against Covid-19.

Though Ms. Goebel said she had been vaccinated herself, she expressed worry about the risks for her children, in part because of the relatively small size of trials in children and the lack of long-term safety data so far. She said the potential risk from a new vaccine seemed to her to outweigh the benefit, because young children have been far less likely to become seriously sick from the virus than adults.

“We absolutely are not ready,” she said…

About 20 percent of parents of 12- to 17-year-olds said they definitely did not plan to get their child vaccinated, according to polling by the Kaiser Family Foundation published last month. The “definitely not” group grew to about 25 percent in parents of children ages 5 to 11, and 30 percent among parents of children under 5.