The White House coronavirus task force on Tuesday urged state leaders to be ready to begin rolling out COVID-19 vaccination efforts for kids as early as the start of next month.

Administration officials told governors on a regularly scheduled call that school-aged kids could be eligible for the shots by early November and encouraged states to have plans in place to get them vaccinated, a source on the call confirmed.

ABC News first reported that pandemic response coordinator Jeff Zients told governors the White House has enough supply to inoculate roughly 28 million kids between the ages of 5 and 11.

Pfizer last week said it had submitted an application to the Food and Drug Administration (FDA) for emergency use authorization of its COVID-19 vaccine in children ages 5 to 11. An FDA advisory committee is meeting to discuss the application on Oct. 26.

White House press secretary Jen Psaki said Wednesday the administration is preparing messaging and outreach strategies to meet parents where they are and address any concerns or questions about getting their children vaccinated once the shot is approved.

"Parents are going to want to go and ask their doctor questions, ask their pediatrician questions, better understand the safety, the efficacy of the vaccine," Psaki said at a press briefing. "What we will be doing is of course ... empowering local medical experts, pediatricians, doctors who can speak to this, who can answer questions as they have them. We’ll be encouraging people to speak to their doctors."

Pfizer has tested a dose for children that is one-third the amount used in adults. Late last month, it announced positive results from its studies, pointing to a “favorable safety profile and robust neutralizing antibody responses.”

Children generally do not get severely ill with COVID-19 as much as older people do, but there were still almost 175,000 cases among children in the week ending Sept. 30, according to the American Academy of Pediatrics, with the highly transmissible delta variant driving a rise in cases among young people in recent months.