The refunds will apply to people who bought tickets before the FAA shutdown began on July 23 and then traveled during the shutdown. Passengers who bought tickets after the shutdown began didn’t pay the taxes anyway. They paid higher fares instead.

The refunds won’t happen right away. Delta said it is waiting for guidance from the IRS about how to handle that.

Last week the IRS said airlines could issue direct refunds. Delta is the first to say it will do so. Other airlines have been referring travelers to the IRS for refunds. The IRS has said passengers who can’t get a refund from their airline will eventually be able to submit a claim to the IRS along with proof of taxes paid and travel dates.

During the shutdown, all the major airlines stopped collecting federal taxes that can add up to $60 on a $300 round-trip ticket. Instead, they raised fares by the amount of the taxes. Travelers are paying the same now as they did before the FAA shutdown, but the money — some $30 million a day for the industry — is going to airlines instead of the government.

Some members of Congress have been pressuring the airlines to roll back the fare increases or to set them aside in an escrow account. The airlines have declined.

Shares of Atlanta-based Delta Air Lines Inc. fell 7 cents to $7.82 in afternoon trading.