WASHINGTON (AP) — The U.S. government's top public health leaders on Tuesday shot down assertions by President Donald Trump that the coronavirus pandemic is under control and the U.S. is excelling in testing for the virus.

The pandemic that Trump has said is "fading" is actually surging in many states, they said, and the need to expand testing is "critical." Dr. Anthony Fauci and other public health authorities also refuted Trump's statement that he told them to ease up on testing because it looks bad to bring more sickness to light.

They also made clear that the rise in cases recently is not just from increased testing, as Trump and Vice President Mike Pence repeatedly suggest, but also from states relaxing their precautions.

Summoned to a congressional hearing, the federal officials gave a measured view of the course of a pandemic that has killed more than 120,000 people in the U.S. They described its progress in sober terms, in contrast with Trump's premature declarations of victory and his bullish posture on getting businesses and schools back open.

A sampling of how Trump's recent statements compare with the scientific appraisals that emerged from the hearing:

TRUMP: "Cases up only because of our big number testing. Mortality rate way down!!!" — tweet Tuesday as the hearing progressed.

THE FACTS: No, increased testing does not fully account for the rise in cases. People are also infecting each other more than before as social distancing rules recede and "community spread" picks up. This was known before the hearing and reinforced in the testimony.

"One of the things is an increase in community spread, and that's something that I'm really quite concerned about," Fauci, the government's top infectious disease expert, testified Tuesday.

As for mortality coming down, Fauci said that is not a relevant measure of what is happening in the moment with infections. "Deaths always lag considerably behind cases," he said. "It is conceivable you may see the deaths going up."

Dr. Robert Redfield, director of the Centers for Disease Control and Prevention, testified that "several communities are seeing increased cases driven by multiple factors, including increased testing, outbreaks, and evidence of community transmission."

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TRUMP on the pandemic: "It's fading away, it's going to fade away." — Fox News interview June 17.

THE FACTS: It's not fading and the scientists said it is not about to.

Fauci said the U.S. is "still in the middle of the first wave" and the imperative is to "get this outbreak under control over the next couple of months."

He said the New York City area, once an epicenter, has done notably well in following federal guidelines and bringing cases down. "However, in other areas of the country we're now seeing a disturbing surge of infections."

New infections per day recorded nationally rose by 30,000 several days ago, he said, after the trend had gone down to as low as 20,000 or so and plateaued there temporarily. "That's very troublesome to me."

The next few weeks "are going to be critical in our ability to address those surgings that we are seeing in Florida, in Texas, in Arizona and other states," Fauci said. "They're not the only ones that are having a difficulty."

Fauci added: "Certainly there will be coronavirus infections in the fall and winter because the virus is not going to disappear."

Said Redfield: "As we get to the fall, we're going to have influenza and COVID at the same time."

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TRUMP: "We have got the greatest testing program anywhere in the world." — remarks Tuesday.

TRUMP: "We've done too good a job." – interview Monday.

THE FACTS: The U.S. is nowhere near the level of testing needed to stem the virus, according to his own health experts.

Redfield testified that health officials are still working to significantly increase testing capacity, calling such expansion a "critical underpinning of our response."

The U.S. currently is conducting about 500,000 to 600,000 tests a day. Many public health experts say the U.S. should be testing nearly twice as many people daily to control the spread of the virus. Looking to the fall, some experts have called for 4 million or more tests daily, while a group assembled by Harvard University estimated that 20 million a day would be needed to keep the virus in check.

Redfield said the U.S. was aiming to boost testing to 3 million daily by "pooling" multiple people's samples, a technique that is still under review by the FDA. He stressed the need for expanded surveillance because some people who get infected may not show symptoms.

"We still have a ways to go," Redfield said.

The U.S. stumbled early in the pandemic response as the CDC struggled to develop its own test for the coronavirus in January, later discovering problems in its kits sent to state and county public health labs in early February.

It took the CDC more than two weeks to come up with a fix to the test kits, leading to delays in diagnoses through February, a critical month when the virus took root in the U.S.

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TRUMP: "You know testing is a double-edged sword. ... Here's the bad part. When you test to that extent, you are going to find more people, find more cases. So I said to my people, 'Slow the testing down please.'" — Tulsa, Oklahoma, rally Saturday.

THE FACT: His people at the hearing said he told them no such thing.

"I know for sure that to my knowledge, none of us have ever been told to slow down on testing," Fauci said. "That just is a fact."

"No," said Redfield when the witnesses were asked if Trump had told them to reduce testing.

"No, sir," said Dr. Brett Giroir, who served as the White House testing coordinator.

"No, congressman," said Dr. Stephen Hahn, commissioner of the Food and Drug Administration.

Several Trump aides said after the rally that his remark about slowing tests was a joke. Trump contradicted them Tuesday, saying "I don't kid."

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AP Health Writer Matthew Perrone contributed to this report.

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EDITOR'S NOTE — A look at the veracity of claims by political figures.

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