ALBANY – President Donald Trump met Tuesday with New York Gov. Andrew Cuomo to discuss how the state and federal government should divide responsibilities for COVID-19 testing as they examine how best to reopen the economy.

Cuomo, a Democrat, requested a meeting with the Republican president at the White House, where the two men spoke in person before Trump joined the White House Coronavirus Task Force for its daily briefing.

After the meeting, Cuomo said he spoke to Trump about two issues: Testing, and providing stimulus funding directly to state governments.

Cuomo, who traveled to Washington after delivering a briefing in Buffalo Tuesday morning, said the meeting "went well" and "was productive."

The two officials agreed to have the state administer the testing system and decide when and how to test residents, while the federal government will work to spur manufacturers to produce more materials for testing kits.

The goal of the partnership is to double the state's daily capacity for COVID-19 testing from the current 20,000 to 40,000, Cuomo said.

"That is an intelligent division of labor, in my opinion," Cuomo said Tuesday evening at the state Capitol after returning from the White House. "Let each level of government what it does best.

Earlier in the day, Trump said he and Cuomo reached an "understanding" on testing.

"We had a very good meeting," Trump said.

For days, Cuomo has called on the federal government to take on a more active role in expanding coronavirus testing capacity so states can be in a better position to reopen their economies.

Specifically, Cuomo wants Trump to take control of the national supply chain to ensure states have enough chemical reagents and supplies to enact a broad testing program before people can go back to work.

Cuomo had previously pledged to oversee the testing programs and determine how tests are allocated, as well as tracing contacts of people who test positive.

At a White House coronavirus briefing after meeting with Cuomo, Trump said the two had a "very productive" meeting.

The president said he believes the model — states handling testing while the federal government works on the supply chain — can work well across the country.

“The federal government will work along with the state on the national manufacturers and distributors," Trump said. "Together, we will all work together.”

Trump also said he spoke with Cuomo about the USNS Comfort, the 1,000-bed Navy hospital ship that has been docked in the New York City harbor in recent weeks.

The president said Cuomo agreed to allow the ship -- which was sparsely used after being altered to treat COVID-19 patients -- to return to its base in Virginia as the spread of the virus slows in New York City.

Cuomo said Trump was "inquisitive" about what the state was doing on testing. He said Trump seemed "deferential" to the state's approach.

The governor's prior remarks on testing drew a rebuke from Trump last week.

When Cuomo forcefully called on the federal government to step up Thursday and help states administer a robust testing program, Trump sharply criticized Cuomo via tweet while the governor was delivering a coronavirus briefing.

That drew a 16-minute response from Cuomo, who strenuously outlined the areas he thought the federal government was performing well and which areas the federal response was lacking.

But Trump and Cuomo appeared to clear the air since then, with Trump asserting Monday that the two work well together.

After their meeting, Cuomo said he and Trump aren't letting their emotions get the better of them.

"Look, for the president and for myself, this isn't about anyone's emotions about anyone else," Cuomo said on MSNBC. "Who cares what I feel, what he feels? We have a tremendous job that we have to get done."

This week, New York is testing a representative sample of 3,000 state residents to see if they have the antibodies for COVID-19, which in theory would give the state a better sense of how many people have contracted and resolved the virus at the center of a global pandemic.

Cuomo's White House visit came as Congress considered a fourth package of federal coronavirus aid, with the Senate voting Tuesday in favor of a measure totaling $484 billion.

The package includes funding to replenish the depleted Payroll Protection Program for small businesses, and is also expected to include direct aid for hospitals and a state-federal testing program.

Cuomo has repeatedly called on Congress to provide direct, unrestricted funding to state governments, warning the state is expecting to come up billions of dollars short of its original tax revenue projections.

The governor's visit also came as Trump faces pressure from New York leaders to pick up the state's share of any FEMA emergency work performed under disaster declarations.

In general, FEMA picks up 75% of the cost and the state picks up 25% for such work.

In an April 11 letter to Trump, U.S. Senate Minority Leader Charles Schumer of New York urged FEMA to pick up the whole cost.

"While New York has drawn down a significant amount of support from FEMA, due to being the epicenter of the pandemic, it also means the New York is on the hook for more money than any other state," Schumer wrote.

Cuomo said he discussed the FEMA issue with Trump and Treasury Secretary Steven Mnuchin. Trump was receptive, Cuomo said.

"The president said he understood and that he would take care of it, and I believe that he will," Cuomo said.