The US president has met the governor of New York have met after weeks of disagreements over the handling of the coronavirus pandemic.
Donald Trump hosted Andrew Cuomo at the White House on Tuesday for discussions described as “honest and open”.
Mr Cuomo told MSNBC: “I wanted to have a face-to-face conversation, particularly on testing.
Coronavirus: Infection numbers in real time
“We have to get this ironed out – this is a very big issue.”
New York has reported 257,000 cases of COVID-19 and nearly 20,000 deaths – almost half of the US total.
More than 45,000 people have died nationwide, with more than 810,000 confirmed cases.
Mr Trump described the meeting as “productive”, also agreeing the federal government would help obtain chemical reagents and other supplies so New York could double its testing for the virus.
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On Tuesday, the Senate also approved $484bn (£393bn) of relief for the economy and hospitals aimed at helping them survive the coronavirus crisis.
Mr Cuomo said this would not help the states, which are “in desperate shape”.
He added: “The president seemed very open and understanding of that and said the next piece of legislation that passes he’s going to be open to that.”
Meanwhile, more states are planning to ease restrictions so people can return to work and economies can begin to recover.
Georgia is one of half a dozen, mostly southern states, that are reopening for business.
Gyms and hair salons are among the businesses that will reopen in the state on Friday, with cinemas and restaurants following next week.
The move comes despite fears that reopening too early could spark a second wave of coronavirus infections.
Centers for Disease Control Director Robert Redfield told the Washington Post: “There’s a possibility that the assault of the virus on our nation next winter will actually be even more difficult than the one we just went through.”
New Jersey, Pennsylvania and Michigan all reported their highest single-day death tolls – more than 800 between them, while the governor of California, the most populous state, has said it is too soon to weaken restrictions there.
Experts have said the the US should be testing three million people per week for a good idea of how far the virus has spread.
However, states have only managed a third of this number in the past week, according to the Covid Tracking Project.
President Trump has also revised his promise to temporarily suspend immigration to put “unemployed Americans first in line for jobs”.
The ban, expected to be approved on Wednesday, will last 60 days and apply to those seeking “green cards” for permanent residency.
It would not affect people coming to the US on a temporary basis.
Around 462,000 immigrant visas were issued in the 2019 fiscal year but, at a time of flight restrictions and border closures around the world, immigration is effectively frozen anyway.