(Reuters) - Major airlines on Monday said demand for flights seemed to be holding up despite concerns that automatic U.S. spending cuts and rising taxes would hurt travel.

Delta Air Lines told a J.P. Morgan investor conference it hoped to post a profit for the first quarter, which would represent the carrier's first March quarter in the black since 2000.

Unit revenue, a key measure that represents passenger revenue per available seat mile, is expected to rise between 4.5 percent and 5.5 percent in the first period, Delta added. It said results were being aided by corporate market share gains and better performance on European routes.

"Our corporate revenues in the first two months of this year are up 8 percent despite the fact that our overall flying levels are down 5 percent," Delta President Edward Bastian said.

Southwest Airlines Co said it expects unit revenue to increase in the low-single-digit percentage range for both the month of February and the first quarter.

Chief Financial Officer Tammy Romo said March bookings looked "solid" for Southwest despite concerns that the effects of automatic U.S. spending cuts known as sequestration, and rising consumer income taxes, would hurt demand.

"At least so far, trends seem to be holding up," Romo said.

U.S. airlines have merged, cut unprofitable routes and raised ticket prices to recover in recent years. Carriers have also created new revenue streams with baggage and food fees.

Shares of major airlines rose on Monday, with Delta and United Continental both up more than 5 percent in late afternoon trading. Southwest was up 2 percent to $12.06 and US Airways Group gained 2 percent to $13.89. JetBlue was up 3.3 percent to $6.36.

US Airways Chief Executive Doug Parker, whose carrier plans to merge with AMR Corp's American Airlines this year and create the world's largest carrier, said the new airline would be able to compete with Delta and United on an equal basis and would look to expand its reach to business passengers.

"This is not an airline that's going to be built on a cost advantage vs. United and Delta," Parker, who will be CEO of the new American should the deal be approved, told the conference. "The value is in running a better airline and doing better on the revenue front than they can."

JetBlue Airways , whose operations were hobbled when Superstorm Sandy barreled through the U.S. Northeast last year, said its February unit revenue was weaker than expected as families recovering opted not to take extra trips.

But Chief Executive Dave Barger said "March is really strong," citing benefit from the shift of the Easter holiday into this month from April last year.

(Reporting by Karen Jacobs; Editing by Gerald E. McCormick and Nick Zieminski)