Governors in US states hardest hit by the coronavirus pandemic have sparred with President Donald Trump over his claims they have enough tests and should quickly reopen their local economies, as more protests are planned over the extension of stay-at-home orders.
New York saw hospitalisations decline to 16,000 from a high of 18,000, and the number of patients being kept alive by ventilators also fell.
There were 507 new deaths, down from a high of more than 700 a day.
"If the data holds and if this trend holds, we are past the high point and all indications at this point are that we are on a descent," Governor Andrew Cuomo said at a daily briefing, while urging residents to continue social distancing.
"We showed you can control the beast. But it's only half-time. We still have to make sure we keep the beast down."
To get a baseline of how many people were infected with the novel coronavirus, Cuomo said the state would do the most aggressive antibody testing in the nation in the next week, using a random sample.
New York will test 2,000 people a day, or 14,000 per week, out of the 19 million residents in the state.
The United States has by far the world's largest number of confirmed cases, with more than 740,000 infections and over 40,000 deaths.
It took the US 38 days after recording its first fatality on 29 February to reach 10,000 deaths on 6 April, but only five more days to reach 20,000 dead.
The toll rose to 40,000 from 30,000 in four days after including untested but probable Covid-19 deaths reported by New York City.
Cuomo, along with other governors, are seeking more tests to detect new infections, as well as to test for immunity as part of their plans to reopen their states.
Republican Governor Larry Hogan of Maryland said during a CNN interview that claims by President Trump and Vice-President Mike Pence that states have plenty of tests were "just absolutely false".
Democratic Governor Ralph Northam of Virginia told CNN the idea states have enough tests was "delusional".
The region of Maryland, Virginia and Washington DC is still seeing increasing cases.
New Jersey reported that its new cases rose by nearly 3,900, the most in more than two weeks.
Boston and Chicago are also emerging hot spots, with recent surges in cases and deaths.
Several states, including Ohio, Texas and Florida, have said they aim to reopen parts of their economies, perhaps by 1 May or even sooner.
The governors of Michigan and Ohio said they could double or triple their testing capacity if the federal government helped them acquire more swabs and reagents.
President Trump's guidelines to reopen the economy recommend a state records 14 days of declining case numbers before gradually lifting restrictions.
LIBERATE VIRGINIA, and save your great 2nd Amendment. It is under siege!— Donald J. Trump (@realDonaldTrump) April 17, 2020
Yet the Republican president appeared to encourage protesters who want the measures removed sooner with a series of Twitter posts on Friday calling for them to "LIBERATE" Michigan, Minnesota and Virginia - all states with Democratic governors - from stay-at-home orders.
Governor Jay Inslee of Washington redoubled his attacks on President Trump's call to "liberate" states, saying the president was encouraging people to violate state laws on self-isolating.
"These orders actually are the law of these states," he said.
"To have an American president encourage people to violate the law, I can't remember any time during my time in America where we have seen such a thing."
Demonstrations to demand an end to stay-at-home measures that have pummelled the US economy have erupted in a few spots in Texas, Wisconsin and the capitals of Ohio, Minnesota, Michigan and Virginia.
More than 22 million Americans have filed for unemployment benefits in the past month.
President Trump had touted a thriving economy as the best case for his re-election in November.
On Saturday, several dozen protesters gathered in the Texas capital of Austin chanting "USA! USA!" and "Let us work!"
In Brookfield, Wisconsin, hundreds of demonstrators cheered as they lined a main road and waved American flags to protest at the extension of that state's "safer at home" order.
The demonstrators mostly flouted the social distancing rules and did not wear the face masks recommended by public health officials.
US lawmakers are very close to an agreement on approving extra money to help small businesses hurt by the coronavirus pandemic and could seal a deal as early as Sunday, congressional and Trump administration officials said.
Congress established the program last month as part of a $2.3tn coronavirus economic relief plan, but it has already run out of money.
Read more: Latest coronavirus stories