WASHINGTON >> Two of the federal government’s top health officials painted a grim picture of the months ahead today, warning a Senate panel that the United States has not contained the coronavirus pandemic a day after President Donald Trump declared that “we have met the moment and we have prevailed.”

The officials warned of dire consequences if the nation reopens its economy too soon, noting that the United States still lacks critical testing capacity and the ability to trace the contacts of those infected.

“If we do not respond in an adequate way when the fall comes, given that it is without a doubt that there will be infections that will be in the community, then we run the risk of having a resurgence,” said Dr. Anthony S. Fauci, an infectious disease expert and the director of the National Institute for Allergy and Infectious Diseases.

He added that “there is a real risk that you will trigger an outbreak that you may not be able to control” if the economy opens too quickly, “leading to some suffering and death that could be avoided.”

Fauci’s remark, during a high-profile — and partly virtual — hearing before the Senate Committee on Health, Education, Labor and Pensions, along with comments from Dr. Robert R. Redfield, the director of the Centers for Disease Control and Prevention, made clear that the nation has not yet prevailed.

The two men, who have at times appeared at Trump’s side, drew a very different picture of the state of the pandemic than the president’s, who has cheered for a swift reopening, championed protesters demanding an end to the quarantine and predicted the beginning of a “transition to greatness.”

Fauci told senators that a vaccine would not be ready in time for the new school year, that outbreaks in other parts of the world would surely reach the United States and that humility in the face of an unpredictable killer meant erring on the side of caution, even with children who have fared well but have recently shown new vulnerabilities.

“We are not out of the woods yet,” Redfield said, “but we are more prepared.”

The two were among four government doctors — the others were Dr. Stephen Hahn, the commissioner of food and drugs, and Adm. Brett P. Giroir, an assistant secretary for health — who testified remotely during the hearing. Sen. Lamar Alexander, R-Tenn., who like Fauci, Redfield and Hahn is in quarantine after being exposed to the coronavirus, presided from his home in Maryville, Tennessee.

Their downbeat assessments came as the death toll in the United States surpassed 81,000 — a figure that Sen. Tim Kaine, D-Va., noted was “45 times the rate of South Korea.” The hearing — titled, “COVID-19: Safely Getting Back to Work and Back to School” — offered little concrete advice on how that was going to happen. It was the first chance lawmakers have had to publicly question the officials in Congress since Trump declared a national emergency two months ago.

Despite the gloomy predictions for the months ahead, over the long term, the experts drew a somewhat more upbeat picture. Asked by Sen. Mitt Romney, R-Utah, if the scientists would ultimately develop a vaccine, Fauci said: “It’s definitely not a long shot, Senator Romney. I would think that it’s more likely than not that we will.”

And Giroir assured Sen. Bernie Sanders, I-Vt., that his office was determined to see to it that a vaccine “reaches all segments of society regardless of their ability to pay.”

For Redfield, who has largely been sidelined by Trump — at least in the administration’s public response — the hearing was a rare opportunity to speak directly to Americans, though he often seemed at pains not to showcase any disagreements with the president. Fauci, one of the most visible federal health officials and voices in the pandemic, has been out of public view for the past two weeks, since Trump abandoned his daily coronavirus task force briefings. Often the subject of speculation that the president will fire him, Fauci reassured senators that their relationship was intact.

“There is certainly not a confrontational relationship between me and the president,” he said, adding that when he gives Trump advice, “he hears that, he respects it, he gets opinions from a variety of other people.”

The hearing scene was extraordinary. The wood-paneled hearing room, in the Dirksen Senate Office Building, was set up with tables along all four walls, so that senators — some of whom were wearing masks that they removed while speaking — could sit at a reasonable distance apart. Those who participated virtually gave viewers a peek into their private lives. Sen. Patty Murray of Washington, the top Democrat on the panel, looked as though she was talking from her kitchen. Alexander’s dog, a Cavalier King Charles spaniel named Rufus, slept in the background as he spoke.

And the mood was at times tense. Alexander put Democrats on notice not to engage in “finger pointing” and insisted that “even the experts underestimated COVID-19,” referring to the disease caused by the coronavirus. Murray followed that by calling Trump’s response “a disaster,” adding: “The president isn’t telling the truth. We must, and our witnesses must.”

Across the Capitol, House Democrats today unveiled a $3 trillion economic relief measure to respond to the pandemic, including $1 trillion in aid to state, local and tribal governments, another round of $1,200 direct payments to American families, and more money for jobless aid and food assistance.

The measure would also provide a $25 billion bailout for the Postal Service, which has said it is set to run out of cash by September without a lifeline from Congress. Murray used her time to make a pitch for the package, saying Republicans — who have already joined with Democrats in approving nearly $3 trillion in government aid — had not done enough.

“What good is a bridge that only gets you to the middle of the river?” she asked.

There were flash points between the witnesses and the senators, as well. In one sharp exchange, Sen. Rand Paul, R-Ky., pressed his belief that children needed to return to school and told Fauci that his was not the only voice senators would listen to.

“I think we ought to have a little bit of humility in our belief that we know what’s best for the economy,” Paul said. “And as much as I respect you, Dr. Fauci, I don’t think you’re the end-all. I don’t think you’re the one person who gets to make a decision.”

Fauci replied, “We should be humble about what we don’t know,” continuing, “and we really better be very careful, particularly when it comes to children,” because children may not be “immune to the deleterious effects” of COVID-19.

The White House has put out guidelines for states to follow, called “Opening Up America Again,” in planning how to reopen businesses and get people back to work and school. The plan recommends, among other things, that before reopening, states should have a “downward trajectory of positive tests” or a “downward trajectory of documented cases” of the coronavirus over two weeks, while conducting robust contact tracing and “sentinel surveillance” testing of asymptomatic people in vulnerable populations, like nursing homes.

But the guidelines are not mandatory, and many states are reopening without adhering to them, seeking to ease the pain as millions of working people and small-business owners are facing economic ruin while sheltering at home.

Sen. Christopher S. Murphy, D-Conn., complained today that Fauci and the other witnesses were “trying to have it both ways” by saying that states should not reopen too early while giving governors guidance that was “criminally vague.” The CDC has been working on a more specific plan that has been held up by the White House. Murphy demanded to know when it would be released — especially given that states are reopening.

“Is it this week? Is it next week?” the senator asked. Redfield replied that the guidance would be on the CDC’s website “soon,” after it is reviewed by Trump’s coronavirus task force.

“Soon isn’t terribly helpful,” Murphy shot back.