SAN FRANCISCO (CBS SF/AP) — Amid a steady rise of Delta variant cases in the San Francisco Bay Area and tougher local vaccination and masking mandates going into effect each day, the Food and Drug Administration gave full approval to Pfizer’s COVID-19 vaccine Monday, a milestone that could lift public confidence in the shots.

As of Monday morning, more than 8,000 San Jose city employees must now provide proof of their COVID-19 vaccination or get tested for the virus weekly to avoid being placed on unpaid leave.

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The policy, which allows for religious and medical exemptions when it comes to vaccinations, will apply to police officers, firefighters, dispatchers, library and city hall workers and even the mayor. Those who refuse and fail to comply and are placed on non-paid leave won’t be able to use vacation, comp or sick time, according to the policy.

More than 200 million Pfizer doses have been administered in the U.S. — and hundreds of millions more worldwide — since December. But up to now, they were dispensed in this country under what is known as emergency use authorization from the FDA.

“The public can be very confident that this vaccine meets the high standards for safety, effectiveness and manufacturing quality the FDA requires of an approved product,” acting FDA Commissioner Janet Woodcock said in announcing full approval, which comes as the U.S. battles the most contagious coronavirus mutant yet, the delta variant.

Pfizer CEO Albert Bourla said in a statement he hopes the decision “will help increase confidence in our vaccine, as vaccination remains the best tool we have to help protect lives.” The shot now will be known in the U.S. by the brand name Comirnaty.

U.S. vaccinations bottomed out in July at an average of about a half-million shots per day, down from a peak of 3.4 million a day in mid-April. As the delta variant fills hospital beds, shots are on the rise again, with a million a day given Thursday, Friday and Saturday.

Just over half of the U.S. population is fully vaccinated with one of the country’s three options, from Pfizer, Moderna or Johnson & Johnson.

Moderna has also applied to the FDA for full approval of its vaccine. J&J said it hopes to do so later this year.

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Full approval means Pfizer’s COVID-19 vaccine meets the same “very high standards required of all the approved vaccines we rely on every day,” said Dr. Jesse Goodman of Georgetown University, a former FDA vaccine chief. That should help “anyone who still has concerns gain confidence” in the shots.

The FDA’s action may also lead to more vaccine mandates covering students, employees and customers.

“Mandating becomes much easier when you have full approval,” said Dr. Carlos del Rio of Emory University. “I think a lot of businesses have been waiting for it.”

Anxious Americans increasingly are on board: Close to 6 in 10 favor requiring people to be fully vaccinated to travel on airplanes or attend crowded public events, according to a recent poll by The Associated Press-NORC Center for Public Affairs Research.

The delta variant has sent cases, deaths and hospitalizations soaring in recent weeks in the U.S., erasing months of progress.

Dr. Tomás J. Aragón, California’s Public Health officer, said he hoped the approval will dramatically increase the number of state residents getting vaccinated.

“For weeks we have watched cases go up at an alarming pace among individuals who are not vaccinated while the vaccinated are largely protected, especially against severe and long-term illness,” he said. “We know the vaccines work. We know vaccines are safe. We know they save lives.”

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© Copyright 2021 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.