Two of the Trump administration’s top health officials acknowledged Sunday that the country is facing a very serious situation with the onslaught of rising coronavirus cases in several states, striking a far more sober tone than President Trump at this stage of the pandemic in the United States.

Adm. Brett Giroir, an assistant secretary with the Health and Human Services department, and Dr. Jerome Adams, the surgeon general, both emphasized their concern about surging outbreaks, many of them in areas where people have not followed recommended public health guidelines to contain the spread of the virus. Their remarks were in sharp contrast to Mr. Trump’s contention just last week that 99 percent of the cases were “totally harmless” and his boast of the country’s low death rate from the virus.

“We’re all very concerned about the rise in cases, no doubt about that,” Admiral Giroir, the official who has been in charge of the administration’s coronavirus testing response, said on ABC’s “This Week.”

“We do expect deaths to go up,” he said. “If you have more cases, more hospitalizations, we do expect to see that over the next two or three weeks before this turns around.”

Still, Admiral Giroir and Dr. Adams offered up a few optimistic notes. Admiral Giroir said the percentage of positive test results was leveling off, and both officials said that doctors had better tools to treat people who become sick than they did at the start of the pandemic.

They steered clear of recommending widespread lockdowns in states with heavy caseloads where hospitals are becoming overwhelmed. Instead, they said those cities and states should consider closing bars and curtailing mass social gatherings, and they strongly urged the vast majority of people in those hard-hit areas to wear masks.

Masks have become a flash point in some areas of the country, especially among members of Mr. Trump’s political base. The president resisted wearing a mask for months, mocked some people who did, and only wore a mask in public for the first time on Saturday during a visit to Walter Reed National Military Medical Center.

“It’s really essential to wear masks,” Admiral Giroir said. “We have to have like 90 percent of people wearing the masks in public in the hot spot areas. If we don’t have that, we will not get control of the virus.”

The host of “This Week,” George Stephanopoulos, asked him about suggestions by Mr. Trump that there could be some harm in wearing masks.

“There’s no downside to wearing a mask,” Admiral Giroir responded. “I’m a pediatric I.C.U. physician. I wore a mask 10 hours a day for many many years.”

Dr. Adams wore a mask during his entire interview on the CBS program “Face the Nation” even though he was being interviewed remotely from Indiana. He said measures like wearing face coverings were “critically important.”

Earlier in the pandemic, Dr. Adams had discouraged people from buying masks, in part so there would be enough for medical workers, and he had said “masks do not work for the general public in preventing them from getting coronavirus.”

On Sunday, when the host of “Face the Nation,” Margaret Brennan, asked if he regretted saying that masks were not effective in keeping the general population healthy, Dr. Adams replied: “Once upon a time, we prescribed cigarettes for asthmatics, and leeches and cocaine and heroin for people as medical treatments,” adding, “When we learn better, we do better.”

Dr. Adams, one of the highest-ranking Black officials in the Trump administration, was also asked about his recent comments that mask-wearing requirements should be enforced locally and not as a national mandate. He had said, “in the context of the Black Lives Matter movement, when we have people being killed for handing out single cigarettes or for falling asleep in a fast food line, I really worry about over-policing and having a situation where you’re giving people one more reason to arrest a Black man.”

Ms. Brennan asked him on Sunday, “Are you saying that racism makes it too risky to mandate masks?”

Dr. Adams replied, “So, to be very clear, I’m not saying it makes it too risky. I’m saying, if we’re going to have a mask mandate, we need to understand that works best at the local and state level, along with education. We need people to understand why they’re doing it. We need people to understand how they benefit from it, because if we just try to mandate it, you have to have an enforcement mechanism, and we’re in the midst of a moment when over-policing has caused many different individuals to be killed for very minor offenses.”

With record numbers of cases in states like Florida, which on Sunday reported 15,000 new cases, the highest single-day total of any state since the pandemic began, both health officials were questioned about the administration’s reluctance to consider returning to a lockdown in some cities and states.

Asked on “This Week” if states with stark increases in cases, like Florida, South Carolina, Arizona, Texas and Georgia, should consider more stringent measures, Admiral Giroir said “everything should be on the table.” He said closing bars and limiting the number of patrons allowed in restaurants were “two measures that really do need to be done.”

In another interview on Sunday, on NBC’s “Meet the Press,” Admiral Giroir said the rates of people testing positive for coronavirus were “leveling off.”

But, he continued: “I don’t want to underestimate the seriousness of this right now. It’s all hands on deck and we have people in the field assisting essentially every county, every hot spot, so we are in the midst of this and we’re taking it very seriously.”

Dr. Adams struck a similar tone. “Please don’t mistake me for saying we’re happy with where we are,” he said on CBS. “What I’m saying is that we are working with states to make sure we can respond to this incredibly contagious disease. And part of that, again, is making sure we’re slowing the spread, right? People understand the importance of wearing face coverings and good hand hygiene and staying home when they can.”

Appearing on “Face the Nation,” Dr. Scott Gottlieb, a former commissioner of the Food and Drug Administration in the Trump administration, said, “I think things are going to get worse before they get better.”

Dr. Gottlieb pointed to some reassuring signals — in data on mobility and restaurant reservations — that people in some states with rising cases are beginning to take social distancing guidelines seriously. Still, he predicted that “in the South, you’re likely to see an extended plateau” of cases.

Unlike in New York, which had a huge surge early in the pandemic but got it under control relatively quickly, Dr. Gottlieb said, “I think the Southern experience is more likely to mirror Brazil.” That country has been besieged with outbreaks and its case count is second only to the United States. Last week, Brazil’s president, Jair Bolsonaro, who had downplayed the pandemic for months, tested positive for the virus.

Dr. Gottlieb said the states that were now hot spots had reopened too early and “people became complacent, especially younger people — they were going out, not taking precautions.”

He said that the surge in infections in younger people had now begun to spread to more vulnerable populations. “That’s what we’re seeing right now, you’re seeing rising cases in nursing homes.”