New York is among the first states in the country to waive some fees and expenses for people who undergo testing for the coronavirus, as public health officials are increasingly worried that medical bills will discourage the poor and uninsured from getting medical care.

The federal government is also considering paying for care for those affected, possibly based on funds available through federal disaster relief programs. There are “initial conversations,” Dr. Robert Kadlec, a senior official at the U.S. Department of Health and Human Services, told Congress on Wednesday.