Washington (CNN) The nation's top infectious disease expert said Sunday that the United States is "struggling" to get the coronavirus crisis under control and that to say otherwise "would be a false statement."

Dr. Anthony Fauci warned Americans in an interview on CBS that "it is going to be a bad week" ahead as there is an escalation in cases, but that "within a week" or so the number of cases should start to flatten out.

"Are you saying, doctor, despite the deaths that we may see, that mitigation is working, and that you do have this outbreak under control?" CBS' Margaret Brennan asked Fauci.

"I will not say we have it under control, Margaret. That would be a false statement. We are struggling to get it under control, and that's the issue that's at hand right now," Fauci replied.

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He continued: "The thing that's important is that what you see is increases in new cases, which then start to flatten out. But the end result of that you don't see for days or weeks down the pipe."

Fauci said that it was crucial for the coronavirus to get "globally under control," or it could become a seasonal issue. He also said that efforts to obtain a vaccine and the beginning of clinical trials will hopefully mean the US is more prepared if there is a resurgence of the virus.

Fauci's comments followed a warning from officials the day before that the next two weeks will be crucial in the fight to stop the spread of the disease.

"The next two weeks are extraordinarily important," said Dr. Deborah Birx, the White House coronavirus response coordinator, said at a Saturday briefing from the task force. "This is the moment to not be going to the grocery store, not going to the pharmacy, but doing everything you can to keep your family and your friends safe, and that means everybody doing the six feet distancing, washing your hands."

President Donald Trump during that briefing warned of "a lot of death" in the coming weeks -- a sober statement that departs from his previous approach to the virus and desire to reopen the country to normal activity.

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The President has sought to project that his administration has the crisis under control in recent weeks, including during a White House briefing in mid-March.

"It's a very contagious virus. It's incredible. But it's something we have tremendous control of," he said during the briefing. At the time, the number of US cases had just passed 3,000.

Fauci also indicated at the time that the virus wasn't under control, saying at the same March briefing that "the worst is yet ahead for us."

As of Sunday morning, there were at least 312,000 known cases of the novel coronavirus in the US and more than 8,500 people had died, according to a tally by researchers at Johns Hopkins University.

This story has been updated with additional background information and context.