President Trump attacked Dr. Anthony S. Fauci as “a disaster” on Monday and said, despite signs that the nation was headed toward another coronavirus peak, that people were “tired” of hearing about the virus from “these idiots” in the government.

The broadside, during a conference call with campaign staff just two weeks before Election Day, was hardly the closing message Trump advisers were looking for. It threatened to focus the electorate squarely on the president’s coronavirus response and pitted him against Dr. Fauci, who as the nation’s top infectious disease expert is a career government scientist the public likes and trusts far more than Mr. Trump.

In increasingly vocal terms, Dr. Fauci has been separating himself from the White House and warning Americans to “hunker down” and brace for a difficult winter — a message at odds with Mr. Trump’s repeated, if false, assurances that the nation is “rounding the corner” on a pandemic that has claimed about 220,000 American lives.

“People are tired of Covid,” Mr. Trump complained on the call, which several reporters were invited into. “I have the biggest rallies I’ve ever had. And we have Covid. People are saying: ‘Whatever. Just leave us alone.’ They’re tired of it.”

He added, “People are tired of hearing Fauci and these idiots, all these idiots who got it wrong.”

Dr. Fauci’s cautionary words are borne out by the numbers. More than 70,450 new coronavirus cases were reported in the United States on Friday, the highest figure since July 24, according to a New York Times database. More than 900 new deaths were recorded. And over the past week, there have been an average of 56,615 cases per day, an increase of 30 percent from the average two weeks earlier.

But beyond pushing for a vaccine, the Trump administration has refrained from confronting the threat aggressively, pushing instead to fully open the economy and get children back in school.

The White House coronavirus task force, which met daily at the outset of the pandemic, now meets about once a week and hosts a weekly conference call with governors, typically to address specific topics like testing and nursing home guidance. Its agenda is largely focused on nuts-and-bolts matters like vaccine reimbursements, state and national stockpiles and whether cruise ships should be allowed to sail.

“The administration’s coronavirus strategy is fundamentally rooted in the bedrock objective of saving lives and helping our country safely open and stay open,” Michael Bars, a White House spokesman, said. “As always, coronavirus-related matters receive appropriate attention, consultation, and input from Task Force experts.”

But the composition of the task force is changing.

Mr. Trump’s pandemic adviser, Dr. Scott W. Atlas, a neuroradiologist with no experience in infectious disease or epidemiology, is a rising power within the White House, embracing a response that calls for allowing the coronavirus to spread naturally while protecting only the most vulnerable. Over the weekend, Twitter removed a post in which Dr. Atlas questioned the efficacy of mask wearing, decreeing it misinformation.

Such ideas have led to internal clashes — and sometimes turf wars — pitting Dr. Atlas against Dr. Fauci and Dr. Deborah L. Birx, the coronavirus response coordinator.

With polls showing the president trailing his Democratic opponent, Joseph R. Biden Jr., the campaign call was supposed to emphasize a big, positive message, especially on the economy, with reporters listening in and most of the campaign staff participating. The call began with Mr. Trump’s campaign manager, Bill Stepien, talking about the Republican ground game and other factors that he said supported Mr. Trump’s path to victory.

Then Mr. Trump erupted.

In addition to proclaiming Dr. Fauci an idiot, Mr. Trump also deemed him a “nice” guy — albeit one who, in Mr. Trump’s view, has stuck around too long.

“He’s been here for 500 years,” the president said, adding: “Every time he goes on television, there’s always a bomb, but there’s a bigger bomb if you fire him. This guy’s a disaster.”

And at a campaign rally in Prescott, Ariz., on Monday, Mr. Trump invoked Dr. Fauci as a way of ridiculing Mr. Biden’s coronavirus plan.

“Biden wants to lock it down. He wants to listen to Dr. Fauci,” the president said, referring to coronavirus-related restrictions on the economy. (Dr. Fauci, addressing a group of pathologists last week, said no one wants to “shut down the country again.”)

The Biden campaign, which has been emphasizing a promise to listen to science over politics, responded with relish: “Mr. President, you’re right about one thing: The American people are tired. They’re tired of your lies about this virus.”

Last week, Dr. Fauci, a career government scientist who has advised six presidents, accused the president’s campaign — though not Mr. Trump himself — of quoting him “completely out of context” and without his permission in a campaign ad. Then, in an interview with the CBS program “60 Minutes” that aired Sunday, Dr. Fauci said he was not surprised that the president had contracted the coronavirus, given the lack of White House precautions.

“Dr.Tony Fauci says we don’t allow him to do television, and yet I saw him last night on @60Minutes, and he seems to get more airtime than anybody since the late, great, Bob Hope,” the president said on Twitter.

Then the president, harking back to Dr. Fauci’s pitch during Opening Day of baseball season here, added a postscript: “P.S. Tony should stop wearing the Washington Nationals’ Mask for two reasons. Number one, it is not up to the high standards that he should be exposing. Number two, it keeps reminding me that Tony threw out perhaps the worst first pitch in the history of Baseball!”

Mr. Trump’s eruption generated a backlash. Senator Lamar Alexander, Republican of Tennessee and the chairman of the Senate Health Committee, called Dr. Fauci “one of our country’s most distinguished public servants.”

“If more Americans paid attention to his advice,” Mr. Alexander wrote on Twitter, “we’d have fewer cases of COVID-19, & it would be safer to go back to school & back to work & out to eat.”

Neither Dr. Fauci nor officials at the National Institute of Allergy and Infectious Diseases, which he heads, responded to a request for comment. But in an interview with The Times last week, before Mr. Trump’s latest comments, Dr. Fauci said he was concerned about the coming months, and resisted the idea that the nation was in a “second wave” because “we have never completely gotten out of the first wave.”

“I have said many times, and I’ll say it again,” he said, “that is not a good position to be in as you enter the cooler months of the fall and the colder months of the winter.”

Since Dr. Fauci emerged as a villain of the political right, he has been assigned a federal security detail. He and his wife, Christine Grady, a bioethicist at the National Institutes of Health, have been threatened by email, phone and text message. They have even been heckled on the street on their nightly walks, though Dr. Fauci is also sometimes stopped by admirers who thank him and ask to take selfies. Their daughters have also been harassed.

Dr. Fauci’s presence at the White House, where he has been a fixture in his decades-long career advising presidents on disease outbreaks, and on television, where he has often appeared to comment on the pandemic, has been severely restricted. Over the summer, Mr. Trump’s press office tried to undermine him with an anonymously attributed list of what it said were his misjudgments in the early days of the coronavirus, which they sent to news media organizations.

In a half-hour tête-à-tête with Mark Meadows, the White House chief of staff, in July, Dr. Fauci confronted him about the move, and about attempts to ignore or block his broadcast media appearances.

During a task force meeting in late September, Dr. Fauci and Dr. Birx confronted Dr. Atlas over a claim he made to the group to support his call for reopening schools and businesses: that parts of the country — including New York — were nearing 40 to 50 percent immunity, which he said would be enough to slow the spread of the virus.

Scientists and public health experts say that would not be enough to achieve widespread immunity. The two demanded he show evidence for the argument, according to two senior administration officials who witnessed the exchange, which was reported earlier by The Washington Post.

After Dr. Atlas arrived at the White House over the summer and gained virtually unfettered access to Mr. Trump, Dr. Birx stopped briefing the president on the pandemic.

Dr. Fauci has also clashed privately with Dr. Atlas over the science behind wearing face masks. Dr. Atlas has told task force members that mask mandates in states such as Hawaii are proof of their futility in preventing infections.

“The role of public policy here is to get rid of the fear, as opposed to what public health officials who are the face of this continue to do, which is instill fear,” Dr. Atlas said in an interview.

“Young people have very low risk of this,” he said. “In fact, for people under 70, the case mortality of this is less than 0.5 percent.”

Mr. Trump has often questioned Dr. Fauci’s recommendations, and frequently dismisses basic health advice, including that people wear masks. At a rally on Sunday and again on Monday, Mr. Trump mocked Mr. Biden for listening to scientists on how to combat the virus. “If I listened totally to the scientists, we would right now have a country that would be in a massive depression,” Mr. Trump said Sunday.

Mr. Trump has also bristled at Dr. Fauci’s superior approval ratings. A poll released late last month by the nonpartisan Kaiser Family Foundation found that 68 percent of Americans trusted Dr. Fauci either a great deal or a fair amount to provide reliable information about the virus, while only 40 percent trusted Mr. Trump.

In the “60 Minutes” interview, Dr. Fauci cited the failure of the president’s staff to take basic precautions at White House events, including the announcement of Judge Amy Coney Barrett’s nomination to the Supreme Court.

“I was worried that he was going to get sick when I saw him in a completely precarious situation of crowded, no separation between people, and almost nobody wearing a mask,” Dr. Fauci said. “When I saw that on TV, I said: ‘Oh my goodness. Nothing good can come out of that. That’s got to be a problem.’ And then sure enough, it turned out to be a super-spreader event.”