As President 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 on 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 days.

They are not the only ones forecasting more carnage. 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 disease caused by the coronavirus, by early August.

The Institute for Health Metrics and Evaluation 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”.

The numbers underscore a sobering reality: While the US 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 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 a “robust testing program” for at-risk health care workers.

But some of the states moving the quickest are not honouring all of those guidelines.

In fact, the Trump administration has steered clear of enacting a national policy to prevent its own projections from coming to pass. On a conference call with the nation’s governors on Monday, Vice- President Mike Pence cheered on state-level coronavirus testing, and he again promised this week to ship out more tests to all 50 states.

But a recording of the call, obtained by The Times, made clear that the White House was taking its cues from state governments. Pence’s upbeat assessment also included some public relations advice for the governors.

“It’s important that as we see progress being made, and declining hospitalisations and emergency room admissions and positive rates going down, that all of these governors are also aware as they’re increasing testing, the number of cases that are going to be reported are going up,” the vice- president said on the call. “But it’s all going to be a matter of making sure that the public sees the whole picture. But it’s all progress.”

While the Trump White House is emphasising testing, experts say a whole range of additional policies are needed to contain the fast-moving virus.

In New York, where the number of overall cases is declining, a cautious-sounding governor Andrew M. Cuomo said Monday that the state would monitor four “core factors” to determine if a region is ready to reopen: the number of new infections; the capacity of the health care system; the testing capacity; and the capacity for “contact tracing” to identify people exposed to those who test positive.

Toll surges past 70,000

US deaths from the coronavirus surged past 70,000 on Tuesday, according to a Reuters tally. Nearly 1.2 million people in the US have tested positive for Covid-19.