Originally Published: 09 MAY 21 10:15 ET

Updated: 09 MAY 21 11:43 ET

By Jason Hoffman, CNN

(CNN) -- The White House Covid-19 response coordinator on Sunday said the country is "turning the corner" on the pandemic, but stressed that despite some Covid fatigue, Americans must get vaccinated and follow the science.

"I would say we are turning the corner," Jeffrey Zients told CNN's Jake Tapper on "State of the Union."

Zients' comments come on the heels of President Joe Biden setting a new goal last week of administering at least one Covid-19 vaccine dose to 70% of the US adult population and having 160 million US adults fully vaccinated by July 4 and as the administration continues to target all Americans as the pace of vaccinations has slowed.

"We're at 58% today," he said, referring the percentage of Americans who have received at least one dose. "So we've got a path ahead of us, which will involve getting people even easier access to the vaccine, making sure that people build their confidence, those who have questions about the vaccine, that we answer their questions, and making sure that we do what we've done from the beginning, which is do this in a fair and equitable way."

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 guidance from the US Centers for Disease Control and Prevention before changing their habits. Calling the US Food and Drug Administration the "gold standard," he also stressed that the three authorized vaccines in the US are safe and effective and that confidence overall in the vaccines increased after the Johnson & Johnson vaccine was temporarily paused.

"We all want to get back to a normal lifestyle," he said. "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. And as we all move toward that 70% goal, they'll be more and more advantages to being vaccinated. And if you're not vaccinated, you're not protected."

If booster shots are ultimately needed for the vaccines, the country will have sufficient supply and be ready for that scenario, Zients told Tapper.

"Look, we're going to look to Dr. Fauci, the FDA, as to the timing and the necessity of a booster shot. If boosters are necessary, we'll be ready, as we have been for all contingencies, and we'll have sufficient supply."