Cuomo, speaking at a briefing after meeting with Trump in Washington earlier in the day, also said the president indicated he would work to get federal funding to states in the next financial aid legislation to be passed by Congress.
With coronavirus-related hospitalizations trending lower in New York, Cuomo has in the past few days turned his attention to the challenge of widespread testing, which he has said would be critical to getting New Yorkers back to work.
Cuomo said Trump had agreed in their White House meeting to have the federal government take charge of securing materials that the manufacturers who supply New York's state labs have struggled to procure from overseas.
The governor added that it was up to his state to help the labs boost their testing capacity and to organize the workforce needed to take more samples from the population.
"That is an intelligent division of labor," Cuomo told the briefing. "Let each level of government do what it does best."
Cuomo said New York would aim to double the number of people it tests each day - including diagnostic and antibody tests - to 40,000. He characterized it as "an enormous undertaking" that would take several weeks, without being specific on timing.