Delta Air Lines is flying high on strong travel demand, particularly from passengers paying for premium seating options.

The company on Thursday morning announced a $1.1 billion profit for its most recent quarter, which ended in September. That's a 59% jump from the same period a year ago.

Revenue from its premium products, such as first-class seating, was up 17%.

CEO Ed Bastian told CNBC that premium revenue "is continuing to drive the strength of the business."

But Delta angered many of its would-be premium customers during the third quarter after announcing an overhaul of its SkyMiles rewards program. The changes would have made it harder to achieve elite airline status and raised the bar for accessing Delta's Sky Club airport lounges.

After a flurry of negative feedback, Bastian conceded, "We probably went too far."

But the plan revisions are not yet clear. In his CNBC interview, Bastian said the airline wants to "make these modifications where people can understand them better."

Based in Atlanta, Delta has one of its largest hubs at Minneapolis-St. Paul International Airport.

Travel was up in all categories during the quarter. Delta's domestic passenger revenue rose 6%; international passenger revenue was up 35%.

Bastian told CNBC that the company has seen an uptick in business travel since Labor Day, driven largely by return-to-office mandates.

"The tech sector and the financial services sector [are] areas that we're seeing double-digit growth," Bastian told analysts in a call Thursday morning.

Delta's total revenue of $15.5 billion was up 10.8% for the quarter, but on Thursday afternoon, its stock price fell about 3%despite beating Wall Street estimates.

On CNBC, Bastian said there is some volatility in the industry as fuel prices increase, and the company has tightened its profit forecast for the rest of the year.

Kyle Potter, executive editor of Minneapolis-based Thrifty Traveler, said that as fuel prices rise, the average ticket cost will climb as well. But he said many regular customers may not feel the impact.

"Fares, especially domestic, have come down pretty considerably," Potter said.

The latest federal consumer price index showed that average fares fell 16% from March to September.

Potter said the uptick in international travel could be a factor in bringing domestic prices down.

Delta is seeing the strongest growth from passengers willing to pay more. Potter said those customers are less likely to feel the sting of any possible economic downturn.

"Domestic strength is really coming from are the premium products domestically," Delta President Glen Hauenstein told analysts in the morning call.

Like many other airlines, Delta has stopped flying into Israel amid the intensifying conflict with Hamas.

"We have suspended our flights through the end of October," Bastian said. "We're going to monitor it very closely."