White House advisors say the U.S. is moving past its peak in COVID-19 infections. However, a top public health official says there's a chance the worst has yet to come.

Robert Redfield, the director of the Centers for Disease Control and Prevention, told The Washington Post on Tuesday that a second wave of the deadly disease is expected to hit this winter, right around the time flu season is in full swing.

"There’s a possibility that the assault of the virus on our nation next winter will actually be even more difficult than the one we just went through," Redfield said. "And when I’ve said this to others, they kind of put their head back, they don’t understand what I mean. We're going to have the flu epidemic and the coronavirus epidemic at the same time."

Redfield explained that having two simultaneous outbreaks of respiratory infections would put a serious strain on the country's health care system. The U.S. reported its first case of the novel coronavirus in early 2020, when flu season had already reached its peak. Redfield told the Post that if the virus had hit earlier in the season, "it could have been really, really, really, really difficult in terms of health capacity."

As of Tuesday, the U.S. had tallied more than 800,000 COVID-19 cases and over 40,000 virus-related deaths. The CDC estimates that from Oct. 1, 2019 through April 4, 2020, there were up to 56,000,000 flu cases and at least 24,000 flu deaths in the U.S.—of that figure, 410,000 –740,000 required hospitalization.

Redfield urged federal and state officials to prepare for a possible second wave later this year, and stressed the importance of social-distancing measures even after the economy reopens. He also reiterated the need for increased testing and contact tracing to slow the spread of the virus. Redfield then encouraged the public to get their annual flu shot to help minimize the number of flu-related hospitalizations. He says the vaccinations "may allow there to be a hospital bed available for your mother of grandmother that may get coronavirus."

During Tuesday's White House coronavirus press briefing, Dr. Deborah Birx addressed Redfield's comments about the severity of a possible second wave.

"I don't know if it will be worse, I think this has been pretty bad," said Birx, a member of the White House Coronavirus Task Force. "When you see what happened in New York, that was very bad. I believe that we'll have early warning signals both from our surveillance that we've been talking about in these vulnerable populations. We're going to continue that surveillance from now all the way through to be able to give us that early warning signals."