(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 masks 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.

3 things that may defeat vaccine hesitancy

The US has an opportunity to get ahead in the Covid-19 pandemic by getting more people vaccinated -- and three key things can help address ongoing concerns, one expert says.

"People were worried about safety. We now have hundreds of millions of doses out there, so we have great data on safety," emergency medical physician Dr. Anand Swaminathan told CNN on Saturday. "People were worried about efficacy," he said, adding there is now real-world data showing how effective the vaccines are.

And finally, Swaminathan said, some Americans were concerned that the vaccines didn't have FDA approval and had only received emergency use authorization. But Pfizer/BioNTech announced Friday an application for full FDA approval of the vaccine for people 16 and older -- making it the first Covid-19 vaccine in the US to be assessed for full approval.

"What's the difference between FDA emergency use authorization and full approval? It's really time and money," infectious disease specialist and epidemiologist Dr. Céline Gounder told CNN on Saturday.

"But for some people, seeing a full approval from the FDA will indeed give them more confidence that these vaccines are safe and effective -- and look, they are safe and effective," she added.

The FDA "will move as expeditiously as possible," without compromising its safety standards, to assess Pfizer's Covid-19 vaccine for approval, Zients said Friday.

More than 151 million Americans -- roughly 45.6% of the US population -- have received at least one Covid-19 vaccine dose, according to CDC data.

More than 112 million Americans -- almost 34% of the population -- are fully vaccinated, CDC data shows.

US official: Vaccine confidence only one piece of puzzle

For officials across the country, getting more Americans vaccinated will now be an uphill battle, as experts say the US has now reached those who weren't as eager to get a shot or still have questions.

Vaccination rates are already falling. For the first time since early March, the seven-day average of Covid-19 vaccine doses administered in the US fell below 2 million per day, according to CDC data published on Saturday. But on Sunday, the seven-day average edged back above 2 million per day, the CDC said.

But confidence in the vaccines is only "one piece of the puzzle," when it comes to the challenges the US faces in its vaccination efforts, US Surgeon General Dr. Vivek Murthy said during a White House Covid-19 briefing on Friday.

"The barriers to getting vaccinated fall into three main categories," he said. "Vaccine confidence, motivation and access."

And local, state and federal efforts are ongoing, he said, which aim to address all three pieces.

"I know it's been a difficult year and that everyone in our country has been asked to step up and sacrifice in a big way," Murthy said. "I want to be clear that this pandemic will end. The faster we get vaccinated, the faster that day will come."

J&J pause 'cast a shadow' on vaccinations

One factor that may have contributed to the slowing vaccinations was the recommended pause on the Johnson & Johnson Covid-19 vaccine, one expert said Saturday.

That recommendation was lifted last month and officials said the label would be updated to warn of blood clot risks. Experts concluded the vaccine's benefits outweighed its "known and potential risks" and the vaccine continued to meet "standards for safety, effectiveness and quality," acting FDA Commissioner Dr. Janet Woodcock said at the time.

But the recommendation to pause had its own effects.

"(The) Johnson & Johnson pause did cast a shadow over the momentum that we had gained," Dr. Jayne Morgan, clinical director of the Piedmont Healthcare Covid Task Force, said.

Two weeks after the J&J recommended pause was lifted, that vaccine accounts for a very small share of doses administered in the US -- and the current pace of administration lags significantly from the pace before the pause, CDC data shows.

Over seven days, the J&J vaccine accounted for just about 3.5% of total doses administered, according to data published Friday by the CDC.

The-CNN-Wire
™ & © 2021 Cable News Network, Inc., a WarnerMedia Company. All rights reserved.