Facing accusations of confusing messaging about the Omicron Covid surge, a senior Biden administration official was forced on to the back foot on Sunday by a supreme court justice’s mistaken remark about hospitalisations among children.

During oral arguments over a vaccinations mandate for private employers, the liberal justice Sonya Sotomayor said on Friday the US had “over 100,000 children, which we’ve never had before, in serious condition and many on ventilators”.

Reporters were swift to point out she was wrong. Though concern about children and Omicron is widespread, the Washington Post cited official data in saying there were “about 5,000 children hospitalised … either with suspected Covid or a confirmed laboratory test”.

According to Johns Hopkins University, more than 836,000 people have died of Covid in the US. More than 206 million Americans, or 62.5% of the eligible population, are considered fully vaccinated.

The Covid response has been dogged by resistance to vaccines and other public health measures stoked by politicians and rightwing media prominently including Fox News.

Nonetheless, critics charge that official messaging has become muddled, not least over the recent decision to cut recommended quarantine from 10 days to five, and confusion about when or if the infected should test again.

Earlier this week, it was reported that Dr Rochelle Walensky, director of the federal Centers for Disease Control and Prevention, was undergoing media training. She also told told reporters she was “committed to improve” communications.

Walensky was interviewed on Fox News Sunday. In Bret Baier, she faced perhaps Fox’s toughest interviewer, after the departure of Chris Wallace. It was not an easy experience.

Baier asked: “The supreme court is in the process of dealing with this big issue about mandates. Do you feel it is the responsibility of the CDC director to correct a very big mischaracterisation by one of the supreme court justices?”

“Yeah,” said Walensky. “Here’s what I’ll tell you. I’ll tell you that right now, if you’re unvaccinated, you’re 17 times more likely to be in the hospital and 20 times more likely to die than if you’re boosted.

“And so my responsibility is to provide guidance and recommendations to protect the American people. Those recommendations strongly recommend vaccination for our children above the age of five and boosting for everyone above the age of 18 if they’re eligible.”

Baier asked if the administration knew how many children were on ventilators.

“I do not have that off the top of my head,” Walensky said. “But what I can say is I don’t believe there are any in many of these hospitals who are vaccinated.

“So really, the highest risk of being on a ventilator for a child is if you’re unvaccinated. We also have recent data out just this week that’s demonstrated that dangerous MIS-C syndrome that we’re seeing in children, 91% protection if you’ve been vaccinated.”

Baier said: “The risk of death or serious illness in children is still very small, right?”

Walensky said: “Comparatively, the risk of death is small. But of course, you know, children are not supposed to die. So you know, if we have a child who is sick with Covid-19, we want to protect them.”

Baier said: “Officially, you emphasise that one of your primary goals was to restore public trust, but do you think it’s fair to say that the trust and confidence of the public has gone down with the CDC?”

“You know,” Walensky said, “this is hard. We have ever-evolving science with an ever-evolving variant and my job is to provide updated advice in the context of rapidly rising cases. And that is what we’ve done and I’m here to explain it to the American people and I am committed to continuing to do so and to continuing to improve.”

Baier said: “We appreciate you coming on, we really do. Just getting facts out there.”

Most observers think the supreme court, tilted 6-3 in favour of conservatives after three appointments under Donald Trump, seems likely to strike down the workplace mandate. The rule is due to come into effect on Monday.

Baier said: “The questioning in the supreme court also said that Omicron was as deadly as Delta. That is not true, right?”

Walensky said: “We are starting to see data from other countries that indicate on a person-by-person basis it may not be. However, given the volume of cases that we’re seeing with Omicron we very well may see death rates rise dramatically.”

Asked if mandates for private employers or government employees including members of the armed forces were necessary if prior infection conferred protection, Walensky said: “I think the thing that’s most disruptive to any business or industry has to have half their workforce out because they’re sick with Covid.”

Such is the case in New York City, where essential services are struggling for staff.

“We have seen with the Omicron variant,” Walensky added, “that prior infection protects you less well than it had … with prior variants.

“Right now, I think the most important thing to do is to protect Americans. We do that by getting them vaccinated and getting them boosted.”