New York Governor Andrew Cuomo has demanded New York City come up with a plan to limit the density of its public areas as weekend crowds appear to ignore officials' warnings to stay indoors and limit contact with other people during the coronavirus pandemic.

He said that "the density level in the city is wholly inappropriate".

"I don't know what they're not understanding", he said during a briefing on Sunday. "This is not life as usual. .... It's insensitive, it's arrogant, it's self-destructive, it's disrespectful to other people, and it has to stop, and it has to stop now. This is not a joke and I am not kidding."

The number of Covid-19 cases in the state has ballooned to more than 15,000, more than half of all confirmed cases in the US, after known infections spiked by more than 4,000 over the weekend. Mayor Bill de Blasio says the city has emerged as the nation's viral "epicentre" as city and state officials clash with Donald Trump over the emergency response.

Governor Cuomo said New York City officials must "come up with a plan" to enforce self-quarantine efforts within 24 hours, suggesting that the crisis could disrupt for up to nine months.

"I'm open to anything, but it has to be done quickly", he said. "How many times can you say you're being reckless and selfish? ... That's us at our best, the community of New York. I need to be able to rely on you. That means you need to be responsible for you and your actions."

He also has asked the US Army Corps of Engineers to immediately erect temporary hospitals in four locations and has called on FEMA to construct four 250-bed field hospitals in New York City, though he warned that the state still is short on supplies and staff to meet what is likely to be a surge in patients in the coming weeks.

The governor told Mr Trump to "cut the red tape, cut the bureaucracy" and work quickly to get emergency hospitals and supplies to states as the number of available beds begins to whittle down and supply stocks diminish.

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Governor Cuomo's blunt, daily updates underline the chasm between increasingly strict local efforts and the federal response, with Mr Trump's daily briefings often containing conflicting information, overconfident claims and denials of responsibility in the midst of a growing crisis.

The governor has urged the president to "immediately" implement the Defence Production Act – which would compel companies to produce relevant equipment and supplies – and nationalise the production of medical supplies, which would relieve New York and other states from competing with other hospital systems for prohibitively expensive equipment.

The governor said: "Time matters, minutes count, this is literally a matter of life and death."

He has also called for New Yorkers to cancel all elective noncritical surgeries, as of Wednesday, which could free up "25 to 30 per cent" of hospital beds.

Hospitals also have been mandated to increase their capacity by 50 per cent but he has asked them to aim to increase their capacity by 100 per cent.

People queue for drive-thru coronavirus testing on Staten Island, New York

Though the majority of deaths in the state have involved people over 70 years old with underlying health conditions, the governor cautioned that as much as 80 per cent of the population could be infected with the virus and to act accordingly.