Big U.S. airlines including Delta Air Lines and American Airlines parent AMR Corp said on Tuesday second-quarter unit revenue would rise, buoyed by recovering business and international traffic and rising fares.

Airline executives believe the clouds have parted for the embattled industry after the 2009 economic downturn and the 2008 oil spike. Shares in the sector rallied on Tuesday, with the Arca Airline index <.XAL> up nearly 4 percent.

We continue to see momentum building in the business, Delta President Edward Bastian told a Bank of America-Merrill Lynch conference that was broadcast over the Internet.

Delta, the world's biggest airline, expects passenger revenue per available seat mile, an important measure, to increase by about 20 percent in the second quarter, while AMR said its quarterly unit revenue including regional aircraft would rise 16.5 to 17.5 percent.

Atlanta-based Delta had said in April it expects a profitable second quarter. On Tuesday, it added that it expects operating margin of 10 percent to 12 percent for the second quarter, higher than its April forecast.

United Airlines parent UAL Corp said on Monday its consolidated unit revenue was also expected to rise by 26 to 27 percent for the second quarter. UAL is planning to merge with Continental Airlines Inc later this year to create the world's industry leader.

The better revenue trends come as business traffic recovers after the industry was battered by economic weakness in 2009. Most major U.S. airlines have cut capacity in the last year and a half to better match supply with demand, and are also able to command higher fares.

Bastian said that while the economy was lifting the industry as a whole, Delta was also benefiting from better international traffic and merger cost savings from its 2008 purchase of Northwest. He said unit revenues in Asia would be up 50 percent for the month of June.

Continental CEO Jeff Smisek told the Bank of America conference that the Delta synergies, expected at the $2 billion level by the end of 2011, bode well for his company's combination with United.

Southwest Airlines Chief Financial Officer Laura Wright cautioned, however, that business demand was still far from pre-recession levels.

Business travel, although it's improving, is still nowhere close to fully recovered, she said.

Wright and other executives said capacity discipline is still necessary. Southwest expects its 2010 capacity to be flat from 2009.

US Airways Group President Scott Kirby told the conference airlines are more likely that ever to resist the temptations of expansion and capacity growth.

I don't think that rapid capacity growth is going to become the problem for the industry at least for the foreseeable future, Kirby said.

Among U.S. airline stocks on Tuesday afternoon, UAL was up 4.1 percent, US Airways gained more than 7 percent, AMR was up 2.7 percent and Delta was up 2.3 percent.

(Reporting by Kyle Peterson in Chicago and Karen Jacobs in Atlanta; Editing by Derek Caney and Matthew Lewis)