The US Department of Transportation did not say how many claims were substantiated, but directed carriers in an enforcement notice "that passengers must be reimbursed immediately when their scheduled flights are canceled or significantly delayed".
The government said it would "exercise its power of prosecution" and allow airlines time to contact customers, update policies and properly train staff.
"The Department is receiving an increasing number of complaints and inquiries from passengers on tickets, including many with non-refundable tickets, which describe having been denied refunds for flights canceled or significantly delayed," the notice said.
Customers can receive a refund when airlines cancel or significantly delay flights. The requirements also apply when government restrictions prohibit flight, the notice said.
The rules do not apply to customers who decide on their own not to fly, for example, out of concern for the coronavirus.
Airlines canceled significant parts of their schedules as demand plummeted. At the end of February, customers were canceling more flights than they booked, according to the Airlines for America industrial group.
Now, industry metrics show that carriers fly about half their schedule and only about 1 in 10 seats are filled.
Mass cancellations mean that airlines owe customers a substantial amount. Worldwide, airlines owe their customers $ 35 billion in refunds and credits in this financial quarter, according to the International Air Transport Association. Different regions have different credit and repayment requirements.
The Department of Transportation's notice said that many passengers have complained about receiving credit for future flights that cannot be used due to deep schedule cuts that extend into the fall.
"As a result, passengers are left with flights and vouchers canceled or significantly delayed and credits for future travel that are not easily usable," says the statement.
Many airline coupons expire after one year. Delta announced on Friday that it would accept credits for coronavirus-related flights for about two years, until the end of May 2022.
A different American agency, the Federal Trade Commission, has received more than 1,600 complaints related to travel and vacations so far linked to the coronavirus, according to FTC data reviewed by CNN. These complaints, including from people seeking their money back on non-refundable trips, allege losses of $ 2.7 million.
The DOT noted that carriers provided refunds, as needed, after incidents, including the September 11, 2001 terrorist attacks.
"Although the public health emergency COVID-19 has had an unprecedented impact on air travel, the airlines' obligation to reimburse passengers for canceled or significantly delayed flights remains unchanged," the agency said.
CNN's Katelyn Polantz contributed to this report.