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At the start of what is expected to be the deadliest week of the coronavirus pandemic in the United States, the White House tried to offer some hope that measures to contain the spread were working.

The virus killed 1,264 over 24 hours in the U.S. as of 2:05 am ET on Tuesday, according to NBC New's tracker. A total of 10,906 have been recorded killed by COVID-19.

Meanwhile China, where the pandemic broke out, claimed that not a single new death was reported, and the city of Wuhan in Hubei province, where the new virus was first identified, prepared for lockdown measures to be lifted.

Dr. Anthony Fauci, the nation's top infectious diseases expert, said on Monday he was "cautiously optimistic" that the worst projections could be avoided "if we keep our foot on the accelerator" — referring to social distancing policies in force throughout much of the country.

Fauci and other officials leading the U.S. response to the crisis emphasized the importance of stay-at-home measures during a briefing.

"I don't think anyone has ever mitigated the way I'm seeing people mitigate right now," he said.

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Nevertheless, President Donald Trump cautioned that over the next week-and-a-half there would be a "big surge" in cases and deaths.

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The president added that his administration was tackling hot spots, including New York, which has been hardest-hit by the virus in the U.S.

"We are pressing into action the full power of American government and American enterprise in our military has been incredible," he said.

While the lockdown was being lifted in Wuhan, the pandemic's original epicenter, a spokesman for China's National Health Commission cautioned the country still faced the risk of new outbreaks caused by domestic and imported cases.

Health officials reported 32 new confirmed cases of the coronavirus in mainland China on Monday, all of them imported, bringing the total to 81,740.

The former epicenter of the epidemic, Wuhan, reported only two new confirmed cases in the past 14 days.

People wearing face masks walk inside a barricaded residential compound in Wuhan, China, on Tuesday. Noel Celis / AFP - Getty Images

On Wednesday, its residents will be able to move in and out of the city for the first time since the city went into lockdown on Jan. 23 to stop the spread of the virus.

For more than two months, Wuhan has been under draconian containment measures with its public transportation completely shuttered and residents ordered to stay inside.

Ahead of the city’s reopening, Chinese state media trumpeted the success of the lockdown measures, praising the residents for their sacrifice, but also warning people against letting their guard down.

“Zero growth does not mean zero risk, and opening a city gate does not mean opening every family door,” Xinhua state news agency said Tuesday.

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The city has been showing signs of going back to normal since last week. With its subway and train service resuming last weekend, some businesses, supermarkets and shopping malls have also re-opened their doors.

Photos shared by state media in the past few days showed people venturing out into the streets, walking their dogs, buying food in the street markets and even relaxing on the banks of the Yangtze River — with many still wearing masks.

But some residents told NBC News they remain cautious about going outside, concerned about a possible second wave of infections.