New York state has recorded 630 more coronavirus deaths, another daily record that takes its toll to 3,565.
Most deaths have been in New York City. The state now has almost as many cases – over 113,000 – as the whole of Italy.
Governor Andrew Cuomo said infections could peak in between four and 14 days.
“Part of me would like to be at the apex and just let’s do it. But there’s part of me that says it’s good that we’re not at the apex because we’re not yet ready,” he said.
Mr Cuomo said the state was continuing its search for more ventilators. He thanked China for sending 1,000 ventilators, which were due to arrive on Saturday. The state of Oregon would deliver 140 more, he said.
In his daily coronavirus briefing, US President Donald Trump said he had assured Mr Cuomo that New York would get the resources it needs.
However, Mr Trump said federal assistance will now be focused on the hardest-hit areas, adding: “There will be a lot of death, unfortunately.”
The US has more than 300,000 confirmed coronavirus cases and more than 8,000 people have died with the virus.
Globally, more than 60,000 people have died and more than 1.1 million have been infected, Johns Hopkins University in the US says.
The state has counted 113,074 confirmed cases, 63,036 of them in New York City.
Mr Cuomo said the number of cases and deaths were now rising at a slower rate in New York City, but there was a worrying increase in cases in nearby Long Island.
Meanwhile a new overflow hospital – the 2,500-bed Javits Center in Manhattan – would be staffed and equipped by the federal government, he said.
Some 85,000 people, about a quarter of them from other states, have signed up to help tackle the outbreak in New York, the worst in the US.
New York City’s mayor has sent messages to its eight million inhabitants urging qualified healthcare workers to volunteer.
“Anyone who’s not already in this fight, we need you,” said Bill de Blasio, appealing for help from “any health care professional: Doctor, nurse, respiratory therapist, you name it”.
Mr de Blasio has estimated that the city needs 45,000 more medical staff to help tackle the pandemic in April and May.
Earlier he urged residents to wear masks – “that could be a scarf or something you make yourself, a bandana” – when they go out.
Speaking at the White House on Saturday, President Trump gave a candid assessment of what lies ahead for the US in the coming weeks.
Next week, Mr Trump said, would “probably be the toughest” yet, warning Americans to brace themselves for “a lot of death”.
To support states in their fight against Covid-19, Mr Trump said his administration would be deploying a “tremendous amount of military, thousands of soldiers, medical workers, professionals”.
The military personnel will “soon” be advised of their assignments, he said, adding that “1,000 military personnel” were being deployed to New York City.
Mr Trump also addressed his use of the Defence Production Act, a Korean-War-era law which gives him powers to control the production and supply of US-made medical products.
He said he was “very disappointed” with 3M, a US company that makes masks, saying it “should be taking care of our country” instead of selling to others.
But he rejected accusations that the US had committed an act of “modern piracy” by redirecting 200,000 Germany-bound masks for its own use.
On the question of easing social-distancing restrictions, Mr Trump reiterated a familiar theme.
“We need to open our country,” Mr Trump said, without giving a timeline. “The cure cannot be worse than the problem itself.”