"If you look at the studies that we at the (National Institutes of Health) are doing in collaboration with the pharmaceutical companies, there will be enough data to apply for an emergency use authorization both by Pfizer, a little bit later by Moderna," Fauci, the director of the National Institute of Allergy and Infectious Diseases, told CNN's Jake Tapper on Tuesday.

"I believe both of them -- with Pfizer first -- will very likely be able to have a situation where we'll be able to vaccinate children. If the FDA judges the data sufficient enough, we could do it by the fall," he added.

Also Tuesday, Pfizer CEO Albert Bourla said data on how the company's Covid-19 vaccine works in children between 5 and 11 should be submitted to the FDA by the end of this month or the first week of October. Vaccine data for younger children will soon follow, he added.

"We are working also on younger kids actually all the way down to 6 months old, between 6 months all the way to 5 years old," Bourla said at an event hosted by the ResearchAmerica Alliance. "Those data will be available a month, month and a half later. So it will be end of October, beginning of November."

Acting FDA Commissioner Dr. Janet Woodcock and Dr. Peter Marks, who heads FDA's vaccine division, said in a Friday statement the agency will carefully review data for a vaccine for children 5 to 11 once it's available and is "prepared to complete its review as quickly as possible, likely in a matter of weeks rather than months."

But "the agency's ability to review these submissions rapidly will depend in part on the quality and timeliness of the submissions by manufacturers," they added.

How to keep children safe

The United States has averaged 171,394 new Covid-19 cases every day over the past week, according to data from Johns Hopkins University. That's a 33% increase from one month ago.

And over the past week, an average of 1,843 Americans have died every day from Covid-19, according to Johns Hopkins data. That's almost triple the average daily death rate from one month ago.

Covid-19 cases are surging among children, too, as schools have welcomed students back -- in many cases without mask mandates. The latest weekly count of new pediatric cases -- 243,373 -- marks about a 240% increase since July, the American Academy of Pediatrics said Monday.

Factors including school reopenings without proper masking have likely contributed to the increase, Fauci said Wednesday.

"Also, we've got to realize that this is happening in the context of the Delta variant, which is remarkably more transmissible, so we're getting more cases in everyone," Fauci said. "When you get a highly transmissible virus that's going around the community, you're going to see a lot more children get infected.

Masks and vaccines are key to keeping children safe in schools, he added.

"If you surround the kids with vaccinated people and you have everybody wear a mask, you can get a situation where the children will be relatively safe in school," Fauci said.

But putting mask mandates in schools remains a heavily debated topic. In New York, two Long Island public school districts are suing the governor and state health commissioner over a statewide school mask mandate imposed ahead of the school year's start.

In Ohio, Gov. Mike DeWine said Tuesday children's hospitals are overwhelmed with Covid and respiratory cases and encouraged schools to issue mask mandates. Just over 54% of the state's public school students are under a mask requirement. The governor said he hasn't implemented a statewide mandate because the state's legislature made it clear they will "take it off" and create further confusion.

"Reasonable people may disagree about a lot, but we can all agree that we must keep our children in the classroom," DeWine said.

In Iowa, a federal judge issued a temporary restraining order Monday that will allow the state's school districts to mandate masks in classrooms. The state will appeal, said Gov. Kim Reynolds, who signed a law in May that bans local entities and school districts from issuing their own mask mandates.

"Today, a federal judge unilaterally overturned a state law, ignored the decision by our elected legislature and took away parents' ability to decide what's best for their child," Reynolds said.

Des Moines Public Schools Superintendent Thomas Ahart called the court's decision "welcome news." Effective Wednesday, students, staff and visitors will be required to wear masks in Des Moines schools, the district said a news release.

Local leaders at odds against mandates

There has been tension in various states over mandates for both vaccines and masking.

Despite Texas Gov. Greg Abbott's restrictions on who can mandate vaccinations, the San Antonio Independent School District has required district employees to be vaccinated against the virus. Texas Attorney General Ken Paxton filed a lawsuit Monday against the district and Superintendent Pedro Martinez over the mandate.

"The decision to openly violate state law and devote district resources to defending Superintendent Martinez's unlawful actions is irresponsible," Paxton said in a news release. "But if school districts decide to use their limited funding to try to get away with breaking the law, my office will oppose them and uphold the rule of law in Texas."

Following President Joe Biden's announcement that businesses of more than 100 employees must require their workforce to get vaccinated or regularly tested, Florida Gov. Ron DeSantis has said that cities and counties in Florida requiring employees to show proof of vaccination or post-infection recovery will face $5,000 fines per violation.

The mayor of Orange County, Florida, said that although the consequences could be costly, the county will not overlook the well-being of its community.

"It could be a lot of money. There is no question about it," Mayor Jerry Demings said at a news conference in reference to the fines. "At the end of the day, it is all of our goal to protect the greater collective of the people in our community, to keep them safe. That's the fundamental role of government."

Debate over booster doses

There is also is a debate over the need for -- and the timing of -- vaccine booster doses.

The Biden administration had announced plans to roll out a third dose as early as next week, pending FDA approval, but some experts say it is not needed yet.

But an international group of vaccine scientists, including some from the US Food and Drug Administration and the World Health Organization, published a paper Monday in The Lancet saying the current evidence does not appear to support a need for booster shots in the general public right now.

The authors of the paper include two senior FDA vaccine leaders, Dr. Philip Krause and Marion Gruber, who will be stepping down in October and November, the FDA announced late last month.

Dr. Peter Hotez, dean of the National School of Tropical Medicine at the Baylor College of Medicine, said he has seen evidence that boosters may "keep people out of the hospital, prevents long Covid ... and could restore interrupting asymptomatic transmissions."

"From the data from Israel, I come out strongly in favor of the boosters," Hotez said.

The FDA is scheduled to meet about boosters Friday, though the agency has been late in getting data to its panel of outside vaccine experts, two sources told CNN.

Committee members will receive materials ahead of the meeting, FDA spokesperson Stephanie Caccomo told CNN.

"Our vaccine team is working around the clock on many priorities, including preparing for Friday's (Vaccines and Related Biological Products Advisory Committee) meeting," she said.