The mounting number of coronavirus cases in many US states and reluctance by parents and school officials to put their children in possible danger of contracting the virus are derailing US President Donald Trump's demand that all public schools must reopen.

Schools across the US are either reopening for the fall, staying closed, turning to online teaching or offering a mix of classroom and virtual learning. The nation's largest public-school districts — New York City with 1.1 million students and Los Angeles with about 735,000 — will not fully reopen their schools.

The number of coronavirus cases in the US is now over 3.7 million, the most in the world and as many as Brazil, India and Russia combined, according to data from Johns Hopkins University. At least 140,000 people have died from COVID-19 in the US.

Speaking on Fox News Sunday, Trump repeated his assertion that the virus will eventually disappear.

"I'll be right eventually," he said. "It's going to disappear, and I'll be right."

The outbreak is so widespread that 18 states have been placed in a so-called red zone because they have more than 100 new cases per 100,000 people per week, according to an unpublished report distributed this week by the White House Coronavirus Task Force, which urged many states to take stricter steps to contain the spread.

The states — Alabama, Arizona, Arkansas, California, Florida, Georgia, Idaho, Iowa, Kansas, Louisiana, Mississippi, Nevada, North Carolina, Oklahoma, South Carolina, Tennessee, Texas and Utah — constitute more than a third of the country.

The Trump administration has made the reopening of schools one of its main priorities as the president seeks to restart the economy in the face of the latest surge in infections with less than four months to go until Election Day on Nov 3.

"If we don't reopen the schools, that would be a setback to a true economic recovery," White House economic adviser Larry Kudlow said on Fox News last week.

The White House and administration officials have insisted that the nation's schools and colleges must physically reopen classes and that online instruction, full or partial, isn't an acceptable alternative. Trump has threatened to withhold federal aid from schools that don't physically reopen.

He also has been critical of online instruction and called the guidelines of the Centers for Disease Control and Prevention (CDC) on reopening schools too "tough" and "expensive".

The Trump administration has been pushing for school-reopening based on the premise that those under age 18 are at low risk if they catch the virus.

While it is unclear how susceptible children are to contracting and transmitting the virus, many parents fear for their children's safety, and teachers say they also worry about a potential health impact.

The New York Times reported Saturday that a large study from South Korea shows that children under age 10 transmit the virus to others much less often than adults do, but the risk is not zero. Those between 10 and 19 can spread the virus at least as much as adults do, according to the study, the Times reported.

"I fear that there has been this sense that kids just won't get infected or don't get infected in the same way as adults and that, therefore, they're almost like a bubbled population," Dr Michael Osterholm, a University of Minnesota infectious diseases expert, told the Times.

"There will be transmission," Osterholm said. "What we have to do is accept that now and include that in our plans."

House Democrats wanted CDC Director Robert Redfield to testify next Thursday at a public hearing on safely reopening schools, but they said Friday that the White House had blocked Redfield and all other CDC officials from testifying.

"Dr Redfield has testified on the Hill at least four times over the last three months. We need our doctors focused on the pandemic response," a White House official said, according to The Associated Press.

In New York, Mayor Bill de Blasio said schools will reopen for at least some in-person instruction in the fall. Proposing three models of staggered in-person instruction, de Blasio's plan would allow for in-person attendance to range from one to three days a week. Students will take classes remotely on the other days.

He also announced that the city will provide free child care to 100,000 students when schools reopen. The city aims to provide relief for working parents who either can't afford to stay home or can't find child care for the days that students aren't in school buildings.

In California, where coronavirus cases are surging and the state is returning to lockdowns of bars, restaurants and offices, Governor Gavin Newsom announced Friday that the state will require schools in counties with high infection rates to remain closed until they can meet public health standards. Los Angeles and San Diego schools will hold classes online this fall.

In Texas, where health department officials on Friday reported a fifth straight day of 10,000-plus confirmed virus cases, education officials relaxed a previous order that would have given public schools three weeks from the start of the fall semester to reopen their classrooms for in-person instruction.

School districts will be allowed to delay on-campus instruction for at least four weeks and ask for waivers to continue remote instruction for up to four additional weeks in areas hit hard by the pandemic. During those second four weeks, districts must instruct at least a small number of students in schools and tell the state what public health conditions would allow them to bring more students into classrooms.

Florida is setting new infection and death records almost daily — like Texas, it reported 10,000-plus cases for five days in a row — and in the hardest-hit counties, officials are considering whether to have half in-person, half-virtual instruction, or fully online instruction.

Governor Ron DeSantis, a Trump ally, has pushed for schools to reopen, making the argument that if Walmart and Home Depot can reopen, schools should, too.

"We have embers and we do have flames," said Trump on Fox News Sunday. "Florida became more flamelike, but it's going to be under control."

Meanwhile, in the sports world, some of the biggest names in the National Football League (NFL) took to social media Sunday to express concerns over the lack of COVID-19 safety protocols in place as teams prepare to open training camps this week.

Super Bowl-winning quarterbacks Drew Brees of the New Orleans Saints and Russell Wilson of the Seattle Seahawks, along with Houston Texans defensive end JJ Watt were among those expressing frustration at the NFL ignoring advice from its own medical experts.

"We need Football! We need sports! We need hope!" tweeted Brees. "The NFL's unwillingness to follow the recommendations of their own medical experts will prevent that. If the NFL doesn't do their part to keep players healthy there is no football in 2020. It's that simple. Get it done @NFL."

Some of those outstanding issues include information about how often players will be tested and what will happen if someone tests positive.

Reuters contributed to this story.