6-8 minutos - Source: BBC
He also said the real US death toll is probably higher than the official figure of 80,000.
His message is at odds with the upbeat tone of President Donald Trump who is keen to get the economy going again.
Dr Fauci was speaking via video to a Republican-led committee of the US Senate.
He was referring to the White House's Opening Up America Again plan, which includes three 14-day phases that states are urged to consider implementing as they allow schools and businesses to reopen.
Several states which are restarting their economies have infection rates that are rising, not falling.
He warned of the risk of triggering an outbreak that officials would not be able to control, adding that such an outbreak would set back economic recovery and lead to "suffering and death".
Although the White House has laid out guidelines for reopening, it is ultimately up to state governors to make the decisions on how to ease the lockdown.
"There is no doubt, even under the best of circumstances, when you pull back on mitigation you will see some cases appear," Dr Fauci warned the US officials.
Questioned about the possibility of a rebound in autumn of the virus, Dr Fauci said one is "entirely conceivable and possible".
"I hope that if we do have the threat of a second wave we will be able to deal with it very effectively to prevent it becoming an outbreak," he said.
Dr Fauci also said there are multiple vaccines in development but "no guarantee" any will be effective, though based on his knowledge of other viruses, he is "cautiously optimistic".
"We have many candidates and hope to have multiple winners," he said. "In other words it's multiple shots on goal."
Meanwhile, Vice-President Mike Pence is keeping his distance from the president after his press secretary Katie Miller tested positive last week.
"The vice-president has made the choice to keep his distance for a few days," said White House press secretary Kayleigh McEnany.
Anthony Fauci's testimony before a congressional committee started as a genteel affair, with senators treating him as a long-serving public health official whose advice carries considerable authority and expertise.
Then Senator Rand Paul spoke.
When it comes to the coronavirus, the Republican from Kentucky said, public heath experts had made "wrong prediction after wrong prediction after wrong prediction".
"As much as I respect you, Dr Fauci," he continued, "I don't think you're the end-all, I don't think you're the one person that gets to make a decision."
Mr Paul went on to assert that "outside of New England", the virus has followed a "relatively benign course". He told Fauci that schools, which have been closed across the US since mid-March, should be reopened as soon as possible.
Mr Paul was giving voice to a growing sentiment among the conservative base that Dr Fauci does not have the nation's - or the president's - best interests in mind.
Crowds of anti-lockdown activists in several states have chanted "fire Fauci", and the director has required special protection after receiving death threats. They, like Mr Paul, have dismissed the spread of the virus beyond the current coastal hotspots, even though data indicates cases are spiking in some areas in the interior of the US.
It's evidence of a growing political divide within the nation over how to respond to the virus and how, and when, to begin easing from existing state-ordered mitigation efforts.
Dr Fauci, for his part, responded coolly.
"I have never made myself out to be the end-all and only voice of this," he told Mr Paul. "I'm a scientist, a physician, and a public health official."
He added that there is still much that is not known about the virus, and warned not to be "cavalier" about the threat to children, given new evidence that they may not be "completely immune to the deleterious effects" of the virus.
Dr Paul, a practising physician, was himself diagnosed with the coronavirus last month and received significant criticism for continuing to work in the Senate after being exposed but before he received his positive diagnosis.
Some US states are beginning to lift lockdown orders. Republican-run states such as Georgia, Oklahoma and Alaska moved first towards relaxing restrictions.
California - America's most populous state - also eased its restrictions on Tuesday. Offices and some restaurants can reopen providing they follow certain precautions, Governor Gavin Newsom said.
What's the situation like in the US?The United States alone has more than 1.3 million confirmed cases, according to the Johns Hopkins University coronavirus tracker - almost six times as many as any other country.
President Trump claimed the US had "prevailed" in testing people for coronavirus infections in a news conference on Monday.
But as of this week, the US has tested only 2.75% of its 330m population, and no state has tested 10% of residents.
In a separate development, White House staff were ordered to wear masks when entering the West Wing after two aides tested positive for Covid-19.
Mr Trump said he did not need to follow the directive as he kept "far away from everyone".