Authorities said, however, there was a slight glimmer of hope that the spread of the Covid-19 outbreak was slowing.
New York state recorded a slight dip in deaths on Sunday compared to the day before, but governor Andrew Cuomo told reporters it was too soon to say whether the pandemic had reached its apex and urged New Yorkers to remain vigilant.
The state of New York reported 594 new coronavirus-related deaths on Sunday, down from 630 announced the day before.
Mr Cuomo said Intensive Care Unit (ICU) admissions and intubations were also decreasing slightly while the discharge rate from hospitals was rising.
Later on Sunday, Mr Trump warned the US was approaching a "horrific point" in the outbreak.
He said: "I think we all know that we have to reach a certain point - and that point is going to be a horrific point in terms of death - but it's also a point at which things are going to start changing.
He added: "We're getting very close to that level right now."
Vice President Mike Pence later added: "We are beginning to see glimmers of progress."
Meanwhile, a Malayan tiger named Nadia at the Bronx Zoo has become what is believed to be the first animal to test positive for the virus in the US, authorities said.
Nadia and six other tigers and lions that have also fallen ill are believed to have been infected by a zoo employee who was not yet showing symptoms, the zoo said.
The US Department of Agriculture (USDA), which confirmed Nadia's test result at its veterinary lab, says there are no known cases of the virus in US pets or livestock.
"There doesn’t appear to be, at this time, any evidence that suggests that the animals can spread the virus to people or that they can be a source of the infection in the United States," said Dr Jane Rooney, a veterinarian and a USDA official.
The USDA said it is not recommending routine coronavirus testing of animals, in zoos or elsewhere, or of zoo employees.
The coronavirus outbreaks around the world are driven by person-to-person transmission, experts say.
Coronavirus: Everything you need to know