The number and rate of coronavirus cases in children have risen since the pandemic took hold in the spring, the Centers for Disease Control and Prevention said in recently updated guidance, underscoring the risk for young people and their families as the new school year begins. 

According to the CDC, the infection rate in children 17 and under increased "steadily" from March to July. While the virus is far more prevalent and severe among adults, the true incidence of infection in American children remains unknown because of a lack of widespread testing, the agency said.

The reminder of children's vulnerability came as the United States reported a seven-day average of more than 1,000 daily coronavirus-related deaths for the 21st straight day. Officials reported 1,220 new deaths and 57,120 new infections Saturday, while public health experts stressed that testing levels remain too low and some states experienced technical difficulties with their data collection.

In an effort to make testing faster and cheaper, the Food and Drug Administration granted emergency use authorization Saturday for a saliva-based coronavirus test, developed by researchers at Yale University, that aims to reduce turnaround times in commercial laboratories.

The test, called SalivaDirect, does not require a swab or a special collection device; a sample can be collected in any sterile container, the FDA said. Nor does it require a separate step to extract nucleic acids, a process that is time-consuming and relies on components that often have been in shortage.

Efficient and reliable testing will be essential this fall as a new academic year increases the urgency of questions about the virus's spread among children.

New York is making progress against the virus after experiencing the country's most severe outbreak in the spring. Hospitalizations have reached their lowest point since March 17, officials said. The state reported a record 88,668 tests Friday, with fewer than 1% coming back positive for the eighth consecutive day.

School closures and other public health measures may have contributed to low rates of coronavirus infections in children early in the pandemic, according to the CDC.

"This may explain the low incidence in children compared with adults," the agency said in its guidance. "Comparing trends in pediatric infections before and after the return to in-person school and other activities may provide additional understanding about infections in children."

Children between 5 and 17 years old also test positive for the coronavirus at higher rates than any other age group, according to CDC data, with positivity rates exceeding 10% in public and private lab tests.

The virus incubation period is the same for children as it is for adults. Children are far less likely to develop severe symptoms, but when they are hospitalized for complications from the virus, about a third are sent to the intensive care unit, the same rate as adults, according to the CDC.

The new academic year could bring new challenges, especially in states where daily infection numbers have increased significantly in recent weeks, such as Hawaii, Illinois and South Dakota. As politicians, district administrators and parents continued to debate the wisdom of resuming in-person learning, schools that have already started offered anecdotal data about the challenges of reopening..

In Mississippi, where most children are returning to school for in-person learning, more than 100 students and staff members have tested positive for the coronavirus in recent days and hundreds more have been forced to quarantine. Nearly half the state's schools have reported cases, the Clarion Ledger recently reported. The state also has the highest daily reported deaths in the country, according to tracking by The Washington Post.

Gov. Tate Reeves, a Republican, said Sunday that the virus spread was not pervasive enough in Mississippi schools to justify any shutdowns. He said the state had plans in place to take action if infections became more widespread, but dismissed concerns about school outbreaks, claiming, without citing specific evidence, that most infected children had contracted the virus from elsewhere in the community.

"Keep this in perspective. We have 300,000 kids in classrooms. We've had approximately 100 cases that have been confirmed positive," he told CBS News's "Face the Nation."

"The point is, no kid, whether they're in school or not, is completely immune from getting the virus," he said. "And so we've got to take measures to make sure that those kids have the opportunity to learn."

In other places where the academic year is beginning, virus concerns have already forced officials to cancel classes or reverse plans to bring students back after attempting to reopen amid the pandemic.

A Nebraska school district on Saturday pushed classes back for a week after three staff members tested positive. Schools in Georgia, Indiana and Tennessee also recently canceled in-person learning after students and employees fell ill with COVID-19, the disease caused by the novel coronavirus.

In Arizona, a school district that voted to resume in-person learning despite missing state health benchmarks paused its reopening indefinitely after teachers threatened not to show up, citing fears about the virus's spread.

"We have received an overwhelming response from staff indicating that they do not feel safe returning to classrooms with students," Gregory Wyman, the district superintendent, said in a note to parents over the weekend.

The series of false starts doesn't bode well for districts that have moved forward with in-person reopening plans advocated by the Trump administration, which has insisted that a full-fledged return to school is essential for children's academic and social well-being.

White House officials have continued to press their case for reopening schools. Jared Kushner, the president's son-in-law and senior White House adviser, told "Face the Nation" on Sunday that he did not believe the coronavirus posed serious risks to children and said he and Ivanka Trump had no qualms about their children returning to school.

"We absolutely will be sending our kids back to school," he said, "and I have no fear in doing so."

Former FDA commissioner Scott Gottlieb cautioned against relying on Kushner's comparison of children's deaths from the novel coronavirus to the number who die of the flu each year. In his own interview on "Face the Nation," Gottlieb said the new virus has not been as prevalent in children.

He said that the roughly 330,000 children who have been diagnosed with the coronavirus is probably a significant undercount and that about 3 million are likely to have been infected. Of those, Gottlieb said about 90 have died. By comparison, he said the flu causes about 11 million symptomatic illnesses in children each year and about 400 deaths.

"There's a lot we don't understand about covid in kids," Gottlieb said. "I think we need to be careful about making comparisons to flu, and the death and disease we see in flu, relative to COVID."