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(CNN) — Dr. Anthony Fauci says federal guidance on wearing face coverings indoors may change soon.

Sunday on ABC News, Fauci was asked whether it’s time to start relaxing indoor mask requirements. Fauci replied, “I think so, and I think you’re going to probably be seeing that as we go along, and as more people get vaccinated.”

The US Centers for Disease Control and Prevention will be updating its guidance almost in real-time, as more Americans get vaccinated, said Fauci, director of the National Institute of Allergy and Infectious Diseases.

The CDC relaxed its guidance last month on wearing masks outdoors but still advises both vaccinated and unvaccinated people to still wear masks in indoor public spaces, such as a mall, movie theater, or museum.

“We do need to start being more liberal, as we get more people vaccinated,” he added.

Sunday on CBS’ “Face the Nation,” Dr. Scott Gottlieb, former commissioner of the US Food and Drug Administration, said face mask requirements should be relaxed now that the Covid-19 risk is dropping.

“Certainly outdoors, we shouldn’t be putting limits on gatherings anymore,” Gottlieb said. “The states where prevalence is low, vaccination rates are high, and we have good testing in place, we’re identifying infections, I think we could start lifting these restrictions indoors as well, on a broad basis.”

Lifting pandemic restrictions when they are no longer necessary will make it easier for public health officials to reimplement them if cases rise again, such as a potential winter surge, Gottlieb said.

Fauci makes a Mother’s Day prediction

The US probably will be back to normal by next Mother’s Day, if enough people get vaccinated against Covid-19, Fauci said on ABC News.

“I hope that next Mother’s Day, we’re going to see a dramatic difference than what we’re seeing right now,” he said. “I believe that we will be about as close to back to normal as we can.”

There are some conditions, he noted.

“We’ve got to make sure that we get the overwhelming proportion of the population vaccinated. When that happens, the virus doesn’t really have any place to go,” he said. “You’re not going to see a surge. You’re not going to see the kinds of numbers we see now.”

White House Covid-19 response coordinator Jeff Zients told Jake Tapper on CNN’s “State of the Union” Sunday that the country is “turning the corner” on the pandemic — but stressed the importance of all Americans getting vaccinated.

He noted that President Joe Biden set a goal of having 70% of adults vaccinated by July 4.

“We’re at 58% today. So we’ve got a path ahead of us,” he said.

Zients said that despite some mask fatigue, Americans should continue to follow the science when it comes to wearing masks indoors, and wait for new CDC guidance before changing their habits.

“We all want to get back to a normal lifestyle. I think we’re on the path to do that, but stay disciplined, and let’s take advantage of the new privileges of being vaccinated and not wearing masks outdoors for example, unless you’re in a crowded place,” he said.