DALLAS >> Two major airlines reported huge second-quarter losses today, and their leaders warned that the new surge in U.S. coronavirus cases has stalled the recovery in air travel and added to their industry’s disarray.

American Airlines posted a loss of more than $2 billion, and Southwest Airlines lost $915 million. That pushed the combined second-quarter loss of the nation’s four biggest airlines to more than $10 billion.

Southwest CEO Gary Kelly said he was encouraged by a pickup in leisure travel during May and June after the dark days of March and April. Southwest added flights for July and August.

Then in the last few weeks a surge in U.S. COVID-19 cases caused bookings to fall, Kelly said. Southwest rewrote its August schedule, dropping some flights.

“We’re just going to have to be prepared to have a lot of volatility and be prepared to make frequent adjustments,” Kelly said, “because it’s really almost impossible to plan right now.”

American — with hub airports in Texas, North Carolina and Arizona and a big operation in Miami — benefited when Sun Belt states eased health restrictions in the spring to boost their economies. Bookings by small and medium businesses in Texas rose from 10,000 in April to 45,000 in June even while corporate bookings were nearly zero, executives said.

The airline added flights in June and July, hoping to capture an increase in summer leisure travel. The gambit apparently worked. However, after Labor Day about 40% of American’s revenue typically comes from business travel.

“It’s pretty unreasonable at this point to think that we’ll be anywhere close to that” this fall, said Vasu Raja, the airline’s chief revenue officer. He said American still plans to increase flying from Dallas-Fort Worth and Charlotte but will trim routes that depend on business travelers.

Analysts believe the April-through-June quarter will turn out to be the industry’s low point. The recovery, however, is likely to be slow and uneven. United Airlines executives said this week that eventually they expect revenue to rise to 50% of last year’s level — they didn’t say when — and stay around that depressed mark until a vaccine is widely available.

Earlier, Delta Air Lines reported a $5.7 billion loss that was worsened by writing down investments in global airline partners that have filed for bankruptcy protection, and United lost $1.6 billion.

U.S. air travel plunged as much as 95% this spring. Between them, American and Southwest carried 15.4 million passengers from April through June. In the same period a year earlier, more than 98 million people jammed on to their planes.

With all those lost ticket sales, airlines have turned to cutting costs and hoarding cash in a desperate bid to hang on until the shadow of COVID-19 passes. They are mortgaging planes and hocking their frequent-flyer programs.

Some airlines are likely to lay off workers in October, when federal payroll help runs out. American has sent layoff warnings to 25,000 employees, United sent them to 36,000, and Delta warned more than 2,500 pilots.

The number of layoffs could be smaller if enough employees take severance packages and quit. At Southwest, which has never furloughed employees, Kelly said he doesn’t expect any layoffs this year because roughly 4,400 employees took buyouts and more than 12,000 will take temporary leaves of absence.

American, based in Fort Worth, Texas, reported a loss of $2.07 billion, compared with a year-ago profit of $662 million. Excluding special items, the loss equaled $7.82 per share, nearly matching the average forecast of 17 analysts polled by FactSet for a loss of $7.84 per share.

Revenue plummeted 86% to $1.62 billion but still beat the analysts’ prediction of $1.44 billion.

CEO Doug Parker called it “one of the most challenging quarters in American’s history.” He said there is “much uncertainty ahead,” but expressed confidence American — the most heavily indebted among U.S. airlines — will pull through.

Dallas-based Southwest’s loss, adjusted to remove special items, worked out to $2.67 per share, slightly better than the analysts’ forecast of $2.73 per share.

Revenue plunged 83% to $1.01 billion. Analysts expected $948 million.

Seattle-based Alaska Airlines said it lost $214 million compared with a $262 million profit a year earlier. Revenue fell 82%.

The airlines had hoped to see stronger demand for travel by late summer. Instead, they have scaled back plans for more flights since U.S. coronavirus cases began surging in June. American said it will operate at 40% capacity from July through September.

“Airlines are starved for cash and profits right now, and they will be quick to add capacity once there is demand,” said Cowen analyst Helane Becker.

United CEO Scott Kirby said this week he expects prices to fall in the short run as airlines fight for passengers. That is already happening — Southwest said its average one-way fare during the second quarter was $134, down from $157 in the same, pre-pandemic period of 2019.