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

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

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 industry measure, to increase by about 20 percent in the second quarter, while AMR said its quarterly unit revenue including regional aircraft should rise 16.5 to 17.5 percent.

Atlanta-based Delta had said in April it expected a profitable second quarter. On Tuesday, it added that it expects operating margin of 10 percent to 11 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.

Kathryn Mikells, UAL's chief financial officer, said the recovery is stronger than expected.

As we've entered the recovery period, I think the recovery was greater than we were able to predict six months ago, she said.

Bastian said that while the economy is lifting the industry as a whole, Delta is also benefiting from better international traffic and merger cost savings from its 2008 purchase of Northwest. He said unit revenues in Asia should 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 Co Chief Financial Officer Laura Wright cautioned, however, that business demand is 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 with 2009.

US Airways Group Inc President Scott Kirby told the conference that airlines are more likely than 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 4.6 percent, US Airways gained 7.8 percent, AMR was up 4.0 percent and Delta was up 3.2 percent.

(Reporting by Kyle Peterson in Chicago and Karen Jacobs in Atlanta; Editing by Gerald E. McCormick and Matthew Lewis)