Cuomo, a Democrat whose state is the epicenter of the US coronavirus epidemic with nearly 20,000 deaths, said the Republican president agreed on a plan for doubling New York's coronavirus screening capacity to 40,000 tests per day.

Under that plan, Cuomo said, the federal government will procure and furnish the test kits and related materials, including the chemical reagents that have sometimes been in short supply.

The state will be responsible for expanding the capacity of some 300 laboratories conducting the tests and hiring the necessary staff.

"That is an intelligent division of labor - let each layer of government do what it does best," Cuomo told a news briefing after his rare face-to-face encounter with Trump, a man with whom the governor has had a testy relationship at best in the media.

He said the testing would mix diagnostic screenings used to determine if someone is carrying the virus, and serology tests in which blood samples are analyzed for the presence of antibodies, an indication of exposure even after an individual is no longer infected.

Cuomo said it will "take several weeks at best" to implement the plan.

"It's in some ways an outrageous goal, but this is New York, and we're used to outrageous," he said, adding that the state's current level of 20,000 tests a day marked the highest per-capita rate for diagnostic coronavirus screening in the world.

As of Tuesday, New York state had tallied more than 257,000 cases of COVID-19, the highly contagious respiratory illness caused by the novel coronavirus. That accounts for more than a quarter of the 809,000-plus known infections nationwide.

Budget shortfall 

Health experts say a massive expansion in both kinds of tests is essential before stay-at-home orders and mandatory business shutdowns, which were ordered to slow the spread of the virus, can be safely lifted.

Cuomo, who said he also stressed the severity of the state's budget problems brought on by the pandemic, described his conversation with Trump as "honest and open."

At a separate White House briefing, Trump called his meeting with Cuomo productive and said he was proud of the relationship his administration has forged with New York.

With social distancing and lockdowns showing results, Cuomo has said he could begin to consider how to reopen a state that ranges from New York City, with more than 8 million people, to farm country and sparsely populated towns.

Trump said the federal government will work with New York to help secure additional capacity for testing, the importance of which the president has at times minimized.

Cuomo also told Trump New York City no longer needed the US Naval Ship Comfort hospital ship to help with overflow patients.

Along with other governors, Cuomo has called on the federal government to provide direct cash assistance to the states, a request that has gone unanswered in the stimulus packages passed by Congress.

New York, facing a $10 billion to $15 billion budget shortfall, needs a cash infusion to pay teachers, police officers, healthcare workers, Cuomo said.

The governor said Trump indicated he understood and promised to "work hard" to obtain funding for states in the next round of legislation.