Donald Trump has warned the US that "there will be a lot of death" this week as he said the country faced its toughest period during the coronavirus pandemic.

He was speaking as Johns Hopkins University said the US now had more than 300,000 cases and the nation recorded its highest single-day death toll from coronavirus on Saturday, with 1,497 dying from the virus in a 24-hour period.

Speaking at his daily White House briefing he said: "There'll be a lot of death, unfortunately, but a lot less death than if this wasn't done ... but there will be death."

He quickly lashed out at the media, accusing unnamed outlets of spreading "false rumours".

The president said "certain media outlets" had to "stop spreading false rumours and creating fear and even panic with the public".

"It's just incredible. I could name them, but it's the same ones. I guess they're looking for ratings."

Mr Trump did not elaborate on which "false rumours" he was referring to. But shortly before the briefing began he tweeted: "@CNN is Fake News. They will take a good story and make it as bad as is humanly possible. They are a JOKE!"

While he offered criticism against organisations like CNN, the president has not criticised Fox News, his news programme of choice, for its own coverage fo the pandemic. Last week 74 journalism professors accused Fox News of being a "danger to public health" for its coverage.

The president went on to complain that state governors were being given more equipment – such as ventilators – than they had even asked for but were still criticising him in the media. He said: "We can't play that game."

The federal government currently has about 10,000 ventilators in the national stockpile. New York and New Jersey are both places the federal government has assisted with ventilators during the pandemic. The rest of the ventilators will go towards other areas of need as needed, the president said.

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One governor mentioned about the ventilator problem was New York Governor Andrew Cuomo. His state has received 4,400 from the federal government but previously requested 40,000, a number the president did not believe was needed despite the governors continual pleas.

Mr Trump said he watched Mr Cuomo's press conference today and thought the governor was just "OK" when it came to graciousness towards the president. "I wouldn't say gracious ... it was OK," he said. "I know he appreciates it. He just can't quite get the words out."

The president added California Governor Gavin Newsom was "very gracious" towards his administration. He also praised how New York City mayor Bill de Blasio has thanked the administration.

And he continued to press the case for hydroxychloroquine, an anti-malarial drug which he has touted as a possible treatment for Covid-19.

He repeated his belief that "the cure can't be worse than the problem itself" and stressed that the US had to reopen for business, without suggesting a specific date.

"What do you have to lose?" Mr Trump said. "It's been out there for a long time. What do you have to lose? I hope they use it."

"I may take it. I have to ask my doctors," he added. Clinical trials launched last month for hydroxychloroquine but there has been no definitive study to show the drug can prevent or diminish Covid-19 symptoms. On Sunday, the FDA authorised emergency use for the drug on Covid-19 patients.

One consistent question the president has received in recent days was if he would implore state governors to shut down their state if they have yet to do so.

Mr Trump was asked again on Saturday why he was not taking a stand against those governors whose states had no stay-at-home orders, and he responded the "Constitution" was what kept him from making those orders.

"We have a thing called the Constitution which I cherish ... I want the governors to be running things. In some cases, we'll supersede," he added.

About 90 per cent of Americans are currently under stay-at-home orders in the US. But states like Utah and South Carolina have yet to issue these orders despite having more than 1,000 cases apiece.

"That's a very small number relative to population," Mr Trump said.

Easter Sunday was mentioned again by the president as something he considered making an exception for to allow people to go to church.

"Maybe we could allow special, for churches, maybe we could talk about it. Maybe we could allow them, with great separation outside, on Easter Sunday. I dunno, it's something we should talk about," he said.

Previously, Mr Trump said he would open up the country by 12 April before reeling that idea back in to say it was just him being optimistic. The president's recent statements about Easter make it unclear if he was actually looking for a "special" exception to allow churches to run next Sunday.

"What we're doing right now I think is going to be very successful," Mr Trump said about mitigation efforts, adding that at a certain point "we have a big decision to make."