New York Governor Andrew Cuomo on Monday extended shutdown in the epicentre of America's deadly coronavirus pandemic until near the end of the month.

Cuomo said the COVID-19 death rate in the state was "effectively flat" for the past two days but announced that schools and non-essential businesses must stay shut until April 29.

"Now is not the time to be lax," he told reporters, adding that fines for violating social distancing guidelines would be increased from $500 to $1,000.

The outbreak has killed 4,758 people in New York state as of Monday morning, Cuomo said, an increase of 599 from Sunday.

On Saturday, New York announced 630 deaths in one day -- it's highest daily total of the epidemic so far.

Cuomo said the number of daily deaths had been levelling off since, suggesting the state may be at the peak of its crisis.

"It is hopeful but it is also inconclusive," he said, warning that the death rate could increase again.

He said it would be a "mistake" to relax restrictions on movement too early.

"If the curve is turning it's because the rate of infection is going down, if the rate of infection is going down it's because social distancing is working. 

"If we are plateauing then we are plateauing at a very high level and there's tremendous stress on the health care system," Cuomo added.

New York has borne the brunt of the spread of COVID-19 in the United States.

Across the country, there have been almost 339,000 cases, according to a running tally by Johns Hopkins University.

In New York state, there have been almost 131,000, Cuomo said.

https://www.youtube.com/watch?v=pOavNaBX4NU