Airline executives said they expect that momentum to continue, allowing them to raise fares to cover soaring fuel costs without undercutting demand.

“In March we saw what’s possible,” with falling infection rates and relaxed restrictions driving a demand resurgence, American Chief Executive

Robert Isom

said during a conference call. “Demand is as strong as we’ve ever seen it.”

United Airlines Holdings Inc.

also said this week it believes the industry has hit an inflection point and expects record revenue in the current quarter and a profitable year. United said it has been able to pass the entire run-up in fuel prices on to consumers.

Both airlines said they are seeing signs that corporate travel—a lucrative segment for airlines—is improving as offices reopen and travel restrictions are lifted. Big corporations are resuming travel more quickly now, United Chief Commercial Officer

Andrew Nocella

said. With fares also on the upswing, United expects its unit revenue for business travel to return to 2019 levels soon.

“After all the debates about the return to business traffic, it is nice to see this important milestone in sight even with many businesses not fully back in the office,” Mr. Nocella said.

Airline executives are hopeful that the easing of a federal requirement that passengers wear masks on flights and in airports will tamp down on disruptive behavior from passengers. Carriers including

Delta Air Lines Inc.,

United and American said this week they’ll start revisiting bans they imposed on passengers who had refused to wear masks, although people whose behavior was especially egregious will likely remain blacklisted.

The carriers’ bullish outlook lifted airlines’ stock prices Thursday. American shares closed 3.8% higher, and United shares climbed 9.3%. Shares of

Alaska Air Group Inc.,

which also reported quarterly results Thursday, gained 0.2%.

For airlines, the first three months of the year were tumultuous. The spread of the Omicron variant of Covid-19 around the holidays and at the start of the year roiled their operations and cut short a nascent travel rebound as U.S. travelers canceled trips, while businesses canceled convention plans and kept workers home.

American Thursday reported a $1.64 billion loss over the three months ended March 31. Stripping out one-time items, the company posted a loss of $2.32 a share. Analysts polled by FactSet were expecting an adjusted loss of $2.39 a share.

As daily new Covid-19 case numbers began to fall, demand for travel returned even as consumers faced higher fares driven by jet fuel prices and labor costs. American’s operating revenue rose to $8.9 billion from $4 billion a year earlier. Analysts polled by FactSet were anticipating $8.79 billion.

Now, one of the biggest questions airlines face is whether they can keep their operations on track as travelers pack planes this summer. Several airlines stumbled last summer and some have shown signs of strain this spring.

Carriers including Alaska,

JetBlue Airways Corp.

and

Spirit Airlines Inc.

have cut schedules recently, moves they said would give their operations more flexibility to handle schedule disruptions. Mr. Isom said American has performed well through the spring break period and has 12,000 more employees now than it did last summer.

“We have sized the airline for the resources we have available,” Mr. Isom said. American said its capacity this year will be a bit lower than it had previously projected due to delays in deliveries of its Boeing 787 jets, but it hasn’t had to throttle back its schedule to adjust for staffing or other constraints. American plans to fly as much as 94% of its 2019 capacity in the current quarter.

United, which has kept its flying schedule smaller throughout the pandemic, said it would increase it gradually in an effort to give priority to reliability.

United Chief Executive

Scott Kirby

said that while United is meeting its pilot hiring goals—bringing in some 200 new pilots each month—an industrywide shortage will be a major hindrance to growth among small and midsize airlines, including the regional airlines that fly to small markets for United.

“This is not a temporary issue,” Mr. Kirby said.

Jet-fuel costs roughly doubled since last April across the country, as Russia’s invasion of Ukraine drove up crude oil prices.

American Airlines

reported a 64.7% increase in jet-fuel prices for the first quarter, to $2.80 a gallon, and the airline is assuming fuel prices of $3.59 to $3.64 a gallon during the current quarter.

Airfares have started to climb in tandem as carriers pass those higher costs on to consumers. Domestic ticket prices in March were 20% higher than 2019 levels, and up 15% from February, according to the Adobe Digital Economy Index.

Adobe said this week that there are signs that the higher fares are starting to curb travel appetite. In the first half of April, domestic bookings online were down 2% from the first two weeks for March, though flight bookings are still ahead of prepandemic levels.

Last week, Delta said those higher costs haven’t kept Americans from traveling. The airline, like American, said it expected to return to profitability in the current quarter amid strong summer sales and bookings.

Mr. Kirby said United isn’t seeing signs that the higher prices are giving consumers pause.

“I don’t think we’re anywhere close to the demand destruction point,” he said.

Write to Alison Sider at alison.sider@wsj.com and Will Feuer at will.feuer@wsj.com