The director of the Centers for Disease Control and Prevention warned Tuesday that a second wave of the coronavirus outbreak in the fall could be worse than the one hitting the U.S. now because it would come at the opening of the flu season.

"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," CDC Director Robert Redfield told The Washington Post. "We’re going to have the flu epidemic and the coronavirus epidemic at the same time."

The COVID-19 outbreak has killed more than 45,000 people in the U.S. and more than 178,000 worldwide, according to the data from Johns Hopkins University.

Many health experts, including Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, have also warned of a possible second wave of infection.

"There is always the possibility as we get into next fall, and the beginning of early winter, that we could see a rebound," Fauci told CNN last week.

Models had predicted that COVID-19, the disease caused by the virus, would kill 100,000 to 200,000 Americans. Though it appears the actual number of fatalities will be much lower – which most experts attribute to the level of adherence to social distancing guidelines – the outbreak has strained the capacity of hospitals to treat the more than 825,000 confirmed cases in the country. States hit hardest by the virus have scrambled to find enough respirators, ventilators and protective gear for medical staff to respond.

This outbreak became widespread in March when the number of flu cases normally begins to taper off. Redfield warned that if hospitals had to respond to another coronavirus outbreak at the same time as flu cases, both of which affect the respiratory system, the health care system could be overwhelmed.

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Redfield said the U.S. was fortunate the coronavirus did not arrive earlier because if the peak from that outbreak had come at the same time as the peak in flu cases, "it could have been really, really, really, really difficult in terms of health capacity."

The CDC director said his concerns about a second wave have largely fallen on deaf ears.

"When I’ve said this to others, they kind of put their head back. They don’t understand what I mean," Redfield told The Post.

Trump quibbled with the Post story, saying Redfield was misquoted during a news briefing Wednesday, and called Redfield to the lectern to explain .

"I didn't say this was going to be worse," Redfield said. "I said it was going to be more complex, or more difficult, and potentially complicated because we'll have flu and coronavirus circulating at the same time."

But when asked whether the Post misquoted him, Redfield said, "I’m accurately quoted in the Washington Post."

Trump repeatedly predicted that if the coronavirus reemerges in the fall, it would "not going to be like it was." He said that any "embers" of the virus that reemerged could be quickly snuffed out. But Trump did not provide details to back up his prediction.

"It's not going to come back on anything near what we went through," he said.

There are many unanswered questions about the virus that could determine whether there will be a second wave of infection and how bad that wave might be. One of the biggest unknowns is whether people who have survived COVID-19 are immune and, if so, how long that immunity lasts.

The virus is similar to other coronaviruses such as SARS and MERS that do convey some immunity, so experts are optimistic this one will do the same. That could mean large swaths of the country will be safe from a second outbreak because many people have likely been exposed to the virus but did not develop symptoms.

The size of the population that might have developed antibodies to the virus can't be known until wider testing has been done. But Fauci told CBS News on Monday that antibody tests won't be meaningful until more is known about the virus.

He said it was "a reasonable assumption that when you have an antibody that you are protected against reinfection. But that has not been proven for this particular virus."

"We don't know how long that protection – if it exists – lasts. Is it one month? Three months? Six months? A year?" Fauci said.

Another key is whether the coronavirus behaves like influenza, largely going away during the warmer months but reappearing as the weather cools, which is the scenario that concerns Redfield.

Redfield said social distancing has been crucial to slowing the spread of the disease. He advised states to adhere to the guidelines put out last week by the White House for them to begin to lift their restrictions. He said the CDC had drafted a detailed guidance for state and local governments on how to begin lifting their restrictions and that it would be made public "shortly."

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When asked about the protests against stay-at-home orders that have been held in multiple states and calls to "liberate" states – language used in a series of tweets from President Donald Trump – Redfield told The Post, "It's not helpful."

In response to The Post's interview, Trump said in a tweet Wednesday that Redfield had been misquoted and would be issuing a statement.

Food and Drug Administration Commissioner Stephen Hahn told CBS News on Wednesday that a second wave of cases was "certainly a possibility" and that it was a concern for all the doctors on the White House coronavirus task force.

Hahn said that was why a key aspect of the administration's plan to reopen the country relies on "surveillance mechanisms to look for the respiratory illnesses and then do the appropriate testing at that time."

"I hope we don't have a rebound. That would make this very difficult, as we get into November," Fauci said. But if there is a recurrence, "hopefully, we'll be able to respond to that rebound in a much more effective way than what we see now."

He said the keys would be developing treatments, expanding testing and the ability to trace who has been in contact with people who have been exposed.

When asked at a briefing Wednesday if she agreed a second wave could be more devastating than the first, Dr. Deborah Birx said she didn't know.

"I don't know if it will be worse. I think this has been pretty bad," said Birx, coordinator of the White House coronavirus task force.

Like Fauci, she said contact tracing should provide "early warning signals" and hoped there would be more treatment options available by then. She also said testing would be important to determine which patients have flu and which had COVID-19 because they are "very close to identical" in the early stages.

Redfield told The Post that about 500 CDC staff members working on various health issues around the country will begin to focus on the coronavirus. He said at least another 650 will be hired to assist with contact tracing and other jobs aimed at helping states move forward and prepare for another potential wave.

An estimate from Johns Hopkins University's Center for Health Security and Association of State and Territorial Health Officials says an additional 100,000 people will be needed to effectively conduct contact tracing for the nearly 330 million people living in the U.S. Those organizations called on Congress to appropriate $3.6 billion in emergency funds for the effort.

A report from former CDC Director Tom Frieden says 300,000 additional hires are needed to do the tracing.

Redfield agreed many more people will be needed to do the surveillance. He told the Post that an option being considered is to train census takers, as well as Peace Corps and AmeriCorps volunteers, to become "part of a comprehensive contact tracing effort."

"These are all discussions that are going on to try to determine what is the optimal strategy to be used," Redfield said.

Another key step to avoid a catastrophic impact from a second wave of the pandemic will be to encourage as many Americans as possible to get a flu shot in the fall. Getting the shot could be the difference in making sure there is "a hospital bed available for your mother or grandmother that may get coronavirus," he said.

Contributing: Elizabeth Weise