U.S. airlines may face a challenging outlook for the rest of the year, but strong travel demand and fourth-quarter capacity cuts are ensuring that airlines fly full airplanes, executives said on Tuesday, and their shares rose sharply.

Delta Air Lines Inc and US Airways Group Inc said they saw no signs that travel was tailing off and forecast solid results for the current third quarter, aided in part by moderating fuel prices.

There clearly appears to be a disconnect between what's going on in customer confidence and consumer sentiment ... and what's going on in the economics of our business, Delta President Edward Bastian told the Deutsche Bank Aviation and Transportation conference in New York. Our revenue momentum is strong.

U.S. airline shares, which hit new lows in the past month, moved up on Tuesday, in some cases dramatically, with the Arca Airline index <.XAL> up 5 percent.

US Airways was up more than 16 percent at $5.64 and Delta rose 8 percent to $7.97. Southwest Airlines Co , American parent AMR Corp and industry leader United Continental Holdings Inc also advanced in a range between 4 percent and about 7.5 percent.

Ray Neidl, senior aerospace sector analyst with Maxim Group, linked the gains to relatively sunny outlooks offered by the airline executives at the Deutsche Bank conference.

If you look at the summary of the different presentations, they were all very positive, especially US Airways, which is up the most, he said. And remember, if you're at a lower number it's easier to get a higher percentage increase.

The airline industry is struggling to recover from a years-long downturn spurred by volatile fuel prices and a global economic downturn that drained travel demand. Airlines have regained stability by consolidating and downsizing to pull excess capacity out of their systems.

US Airways President Scott Kirby on Tuesday said reports of a slowdown in the airline industry, even in the face of an uncertain economy, were overblown.

The demand environment is very robust, Kirby said at the conference. We just don't see any evidence yet of a slowdown.

He added: I think you're going to see strong revenue results across the industry in September and surprisingly good results, particularly in light of what you read in the headlines.

Delta said moderating fuel prices, corporate demand and benefit from an excise tax suspension during the partial U.S. Federal Aviation Administration shutdown over the summer would produce a better-than-expected third quarter. The airline said it expects an operating margin of 9 percent to 11 percent for the period, compared with a July view of 7 percent to 9 percent.

Leaders of major U.S. airlines also told the Deutsche Bank conference that seating capacity would shrink in the next year as economic pressures bear down.

Beverly Goulet, vice president of corporate development at AMR, said her carrier would cut capacity -- the number of seats for sale -- for the fourth quarter by about 0.5 percent.

I think it's fair to say that the environment seems to be holding up pretty well, Goulet said. Our booking levels are pretty consistent with where they were last year.

She also said the carrier would adjust capacity on transatlantic routes for early 2012.

United Continental said it would curb domestic capacity in 2012, while increasing international flights.

Southwest Chief Financial Officer Laura Wright said her company's capacity would be flat or slightly down next year.

Wright added that September bookings were looking good and said her company expects passenger revenue per available seat mile, an important measure, to rise in the low-to-mid-single-digit percentage range in the current third quarter.

(Reporting by Kyle Peterson in Chicago and Karen Jacobs in Atlanta; editing by Andre Grenon and Gerald E. McCormick)