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.

In addition to the nation’s 27.5 million uninsured, some lawmakers are concerned that the tens of millions who are underinsured — Americans with high deductibles or limited insurance — may also be at risk of unexpected expenses as more and more people are exposed to the virus.

The health insurance system “is designed to make you think twice to seek care every time you get a runny nose, fever and cough,” said John Graves, a health policy expert at Vanderbilt University. Even though identifying people with the virus in the early stages is critical to preventing a spread of the disease, Dr. Graves said, many people are likely to wait out any symptoms to avoid expensive care.