WASHINGTON — As President Donald Trump presses states to reopen their economies, his administration is privately projecting a steady rise in coronavirus infections and deaths over the next several weeks, reaching about 3,000 daily deaths on June 1 — nearly double the current level.

The projections, based on data collected by various agencies, including the Centers for Disease Control and Prevention, and laid out in an internal document obtained Monday by The New York Times, forecast about 200,000 new cases each day by the end of May, up from about 30,000 cases now. There are currently about 1,750 deaths per day, the data shows.

Another model, closely watched by the White House, raised its fatality projections on Monday to more than 134,000 American deaths from COVID-19, the illness caused by the coronavirus, by early August. The Institute for Health Metrics and Evaluation (IHME) at the University of Washington more than doubled its previous projection of about 60,000 total deaths, an increase that it said partly reflects “changes in mobility and social-distancing policies.”

IHME’s higher projections “reflect the effect of premature relaxation of restrictions,” said the model’s creator, Christopher Murray. For Washington state, the model’s death estimate jumped from about 800 a few days ago to more than 1,000.

The major revisions in the model include two approaches, one a statistical approach used to project likely deaths in the next eight days, and the other a more classic, epidemiological model that includes information about disease transmission and people’s movements, as well as the potential impact of warming weather that might slow the spread of the virus.

Mobility data from cellphones and computers shows people have been moving around more as social-distancing restrictions have been eased in several states and cities. While some states have boosted testing to find and isolate new cases, those efforts “do not offset rising mobility, thereby fueling a significant increase in projected deaths,” according to a statement from IHME.

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While the United States has been hunkered down for the past seven weeks, the prognosis has not markedly improved. As states reopen — many without meeting White House guidelines that call for a steady decline in coronavirus cases or in the number of people testing positive over a 14-day period — the cost of the shift is likely to be tallied in funerals.

“There remains a large number of counties whose burden continues to grow,” the CDC forecast warned, alongside a map that offered a detailed view of the growth of the pandemic.

The projections amplify the primary fear of public health experts: that a reopening of the economy will put the nation right back where it was in mid-March, when cases were rising so rapidly in some parts of the country that patients were dying on gurneys in hospital hallways amid overloaded health systems.

Under the White House’s reopening plan, called “Opening Up America Again,” states considering relaxing stay-at-home policies are supposed to show a “downward trajectory” either in the number of new infections or positive tests as a percent of total tests over 14 days, and have a “robust testing program” for at-risk health care workers.

While the Trump White House is emphasizing testing, experts say a whole range of additional policies is needed to contain the fast-moving virus: isolation of those infected, contact tracing to locate people who interacted with a coronavirus-positive person and quarantines for those people.

Nationally, 27 states had loosened social-distancing restrictions in some way as of Monday, and others had announced changes that will take effect in the coming weeks, according to an analysis by the Kaiser Family Foundation. But only 20 of those states meet the case­load or testing criteria set out by the Trump administration.

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The remaining seven — Indiana, Iowa, Kansas, Minnesota, Mississippi, Nebraska and Wyoming — are still showing a rise in daily infections and positive tests, but have moved toward reopening anyway.

If anything, the administration’s projections are too optimistic, forecasting experts said Monday. In the projections, the number of actual deaths for one of the last days in April turned out to be slightly lower than what the model showed. But for much of April and parts of May, actual deaths were some 10 times higher than the model predicted.

“The model is overly optimistic and not particularly useful in guiding decisions about the disease’s trajectory,” said Dr. Donald Burke, a professor of epidemiology at the University of Pittsburgh Graduate School of Public Health.

Dr. George Rutherford, a professor of epidemiology at the University of California, San Francisco, noted that the government’s model has already come in below reported deaths from COVID-19, and that death toll is not counting deaths not officially recorded. “Remember,” he said, “these are reported deaths; the true number is likely higher.”

The White House distanced itself from the projections, saying the document, dated May 2, was not produced by or presented to the president’s coronavirus task force, which does its own modeling. “The data is not reflective of any of the modeling done by the task force or data that the task force has analyzed,” Judd Deere, Trump’s deputy press secretary, told reporters on Monday.

The creator of the model said the numbers are unfinished projections shown to the CDC as a work in progress. The work contained a wide range of possibilities, and modeling was not complete, according to Justin Lessler, an associate professor of epidemiology at the Johns Hopkins Bloomberg School of Public Health, who created the model.

He said he didn’t know how the update was turned into a slide deck by government officials and shared with news organizations.

“I had no role in the process by which that was presented and shown. This data was presented as an FYI to CDC … it was not in any way intended to be a forecast,” Lessler told The Washington Post.

Lessler insisted, however, that the numbers show how moving to reopen the country could spiral out of control. He said 100,000 cases per day by the end of the month is within the realm of possibility.

“There are reopening scenarios where it could get out of control very quickly,” Lessler said.

On Sunday, the president offered his own projections, saying that deaths in the United States could reach 100,000, twice as many as he had forecast only two weeks ago.

“We’re going to lose anywhere from 75, 80 to 100,000 people,” he said on Fox News. “That’s a horrible thing. We shouldn’t lose one person over this.”

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White House officials have been relying on other models to make decisions on reopening, including the IHME model and a “cubic model” prepared by the Council of Economic Advisers, led by Trump adviser Kevin Hassett.

People with knowledge of the “cubic model” say it currently shows deaths dropping precipitously in May — and essentially going to zero by May 15.

The largest number of deaths in the United States in a single day since the pandemic began occurred on April 21, when 2,874 people died. (A total of 6,147 deaths were reported on April 14, but they included New York City adding more than 3,000 probable deaths to the daily total.)

To date, 1.16 million people in the U.S. have been infected by the coronavirus and more than 67,000 have died. Both figures are widely believed to undercount the actual totals.

Public health experts and epidemiologists say they were not surprised by the administration’s numbers. Many do not expect the virus to slow down until 60%-70% of the population is infected, creating what experts call “herd immunity.”

In recent days, experts following the course of the pandemic in the United States have begun to predict that the country would be living with a sizable COVID-19 caseload for some time.

Dr. Michael T. Osterholm, the director of the Center for Infectious Disease Research and Policy at the University of Minnesota, published an analysis last week describing three possible pandemic wave scenarios through the end of 2021: a series of repetitive smaller waves that gradually diminish over time; a sharp rise in cases in the fall and one or more subsequent smaller waves; and a “slow burn” of continuing transmission, without a clear wave pattern.

Yet many states are still operating under stay-at-home orders. Public health officials said their goal was to “bend the curve” — to slow and ultimately reverse the rising trajectory of infections — by shutting down schools and businesses. But after nearly two months of a near total shutdown, the curve does not appear to have bent as far as they had hoped.