(Adds reaction from Arizona, Ford, union)

By David Shepardson and Julie Steenhuysen

WASHINGTON, July 27 (Reuters) - Americans fully vaccinated against COVID-19 should go back to wearing masks in indoor public places in regions where the coronavirus is spreading rapidly, U.S. health authorities said on Tuesday.

In a toughening of guidance issued earlier this month, the U.S. Centers for Disease Control and Prevention (CDC) also recommended all students, teachers and staff at schools for kindergarten through 12th grade wear masks regardless of whether they were vaccinated.

U.S. coronavirus cases have been rising due to the highly contagious Delta variant, which emerged in India but has quickly spread and now accounts for more than 80% of U.S. coronavirus cases.

U.S. President Joe Biden said that increased vaccination and mask wearing would help the United States avoid the pandemic lockdowns, shutdowns and school closures that the country faced in 2020. “We are not going back to that,” Biden said.

The CDC said that 63.4% of U.S. counties had transmission rates high enough to warrant indoor masking and should immediately resume the policy. Manhattan, Los Angeles and San Francisco meet the transmission criteria, as does the entire state of Florida, but Chicago and Detroit do not.

American Federation of Teachers President Randi Weingarten praised the new CDC mask guidance in a statement, calling it "a necessary precaution until children under 12 can receive a COVID vaccine and more Americans over 12 get vaccinated."

The CDC's previous guidance for schools only called for unvaccinated students to wear masks.

However, the new CDC recommendations are not binding and many Americans, especially in Republican-leaning states, may choose not to follow them. At least eight states bar schools from requiring masks.

Arizona Governor Doug Ducey, a Republican, rejected the CDC guidance. "Arizona does not allow mask mandates ...,” he said in a statement. "We’ve passed all of this into law, and it will not change."

The United States leads the world in the daily average number of new infections, accounting for one in every nine cases reported worldwide each day. The seven-day average for new cases has been rising sharply and stands at 57,126, still about a quarter of the pandemic peak.

Two months ago, when the CDC announced that fully vaccinated people could shed their face coverings, COVID-19 was on the decline. Vaccinations have since slowed dramatically and only 58% of people eligible are fully vaccinated.

New studies show that fully vaccinated people who become infected carry as much virus as unvaccinated people do, suggesting they may be able to transmit the infection to others, CDC Director Dr. Rochelle Walensky told reporters on a telephone briefing.