Donald Trump has warned America to brace for a “very, very painful two weeks” as the White House projected that the coronavirus pandemic could claim 100,000 to 240,000 lives, even if current social distancing guidelines are maintained.

Striking an unusually sombre tone at the start a marathon two-hour briefing, the US president defended his early handling of the crisis and displayed models that, he said, justified his decision to keep much of the economy shut down.

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“I want every American to be prepared for the hard days that lie ahead,” Trump said at the White House. “We’re going to go through a very tough two weeks. This is going to be a very painful, very, very painful two weeks.”

The US death toll from the coronavirus climbed past 3,800 on Tuesday, eclipsing China’s official count. Trump has been widely condemned for exacerbating the crisis by failing to prepare testing kits, breathing apparatus and other equipment.

On Tuesday his experts said their models showed between 100,000 and 240,000 Americans could die even if the US keeps mitigation measures in place.

Dr Deborah Birx, the White House coronavirus taskforce response coordinator, said models showed a worst case scenario of between 1.5m and 2.2m deaths in the US “without mitigation”.

But with measures in place, she added, the “mountain” could be reduced to a “hill” that projects 100,000–240,000 deaths – still a staggering total. She stressed that the number could be lower if people changed their behavior.

She displayed a chart in which New York had by far the most cumulative cases, followed by New Jersey, then the other 48 states bunched together. Birx expressed hope that social distancing could prevent major outbreaks in those states.

Early mitigation slowing the spread of disease in California and Washington state “gives us great hope”, she added. “It’s communities that will do this. There’s no magic bullet. There’s no magic vaccine or therapy. It’s just behaviour.”

Asked if Americans be prepared for the likelihood that there would be 100,000 Americans who die from this virus, Dr Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said: “The answer is yes. As sobering a number as that is, we should be prepared for it.

“Is it going to be that much? I hope not, and I think the more we push on the mitigation, the less likelihood it will be that number ... We are really convinced mitigation is going to be doing the trick for us.”

He added: “We’re going to continue to see things go up. We cannot be discouraged by that because the mitigation is actually working ... Now is the time, whenever you’re having an effect, not to take your foot off the accelerator and on the brake, but to just press it down on the accelerator. And that’s what I hope and I know that we can do over the next 30 days.”

Trump eventually heeded such advice, and opinion polls, after previously declaring an ambition to restart the economy by Easter. He announced on Sunday that he was extending to 30 April the guidelines that urged Americans to cease social gatherings, work from home, suspend onsite learning at schools and more in a nationwide effort to stem the spread of the virus.

Trump spoke after another bad day for the stock market. The Dow Jones Industrial Average plunged more than 400 points, or roughly 1.9%, to seal the worst first-quarter finish of its 135-year history.

Facebook Twitter Pinterest A shoe company in Culver City, California, makes masks to be donated to hospitals. Photograph: Mario Tama/Getty Images

But the president defended shutting down much of the economy, attempting to rewrite history. Trump, who in speeches and on Twitter has compared Covid-19 to the common flu, said: “A lot of people have said, ‘Ride it out. Don’t do anything, just ride it out. And think of it as the flu.’ But it’s not the flu. It’s vicious.”

And as the briefing wore on, more of the old Trump emerged. He made misleading claims about the early travel restrictions he imposed on China and Europe and, despite complaints from state governors, defended the supply of ventilators and other equipment.

Although public health experts raised the alarm early based on reports from China, the president claimed: “Nobody knew how contagious this was. I don’t think any doctor knew it at the time. People have not seen anything like this.”

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And trying to put his own efforts in a positive light, he noted that without his mitigation guidelines, models show the death toll could have reached 2.2m. “You would have had people dying all over the place.

“You would have seen people dying in airplanes, you would have seen people dying in hotel lobbies. How many people have even seen anybody die? You would have seen death all over.”

The president added: “One hundred thousand is, according to modeling, a very low number.” But he also described the figure as “very sobering”.

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