DALLAS — American Airlines and Southwest Airlines both posted second-quarter profits on Thursday thanks to generous federal pandemic relief that covers most of their labor costs.

The reports on Thursday underscored the progress that airlines are making in rebuilding after the coronavirus hit — and how much farther they must go to fully recover.

American eked out a second-quarter profit of $19 million due to nearly $1.5 billion in taxpayer support. Southwest reported a profit of $348 million, including $724 million in federal help.

Southwest said it made money in June even without the government aid and hopes to be profitable by any measure in the third and fourth quarters if the pandemic worsen.

Southwest CEO Gary Kelly said third-quarter travel bookings are “very strong,” and he sees no impact yet from rising coronavirus cases tied to the fast-spreading delta variant.

“We are very well prepared to manage and muddle our way through if the delta variant affects our business,” he added.

American and Southwest — like Delta and United in the past week — reported revenue far above 2020 levels. That reflects the rising number of people taking flights in the U.S. — now about 2 million a day, or about 80% of pre-pandemic levels. Domestic leisure travel is roughly back to normal, but business and international travelers are still mostly absent.

As passengers stream back, flight delays have soared. The problems have been greatest at Southwest and American, which have struggled with hundreds of delayed flights a day.