Shares of major U.S. airlines slumped Wednesday after Delta Air Lines Inc. said that too many flights on some international routes cut into revenue growth.

Airlines usually increase passenger-carrying capacity by adding flights. Investors worry that fares and profits can fall if the supply of seats on lucrative international routes outstrips travel demand, as has happened before in the airline industry.

Shares of Delta, the nation’s third-largest airline company by traffic, dropped $2.13, or 5.3 percent, to $38.18 in late afternoon trading. Shares of United lost 6.2 percent and American Airlines fell 5 percent.

Delta said that last month’s passenger revenue for each seat flown one mile rose 4.5 percent over June 2013. That figure rises when airlines fill more seats or sell them at higher average fares, and June’s increase could have been seen as an indication that travel demand and airline pricing power remained strong at the start of the peak summer travel season.

But it was a letdown after Delta’s 7 percent increase in the measure in May. J.P. Morgan analyst Jamie Baker said investors expected 6 percent growth in June. Delta said that corporate and U.S. travel remained strong in June but revenue per mile was hurt by a dip in business travel to Latin America during the World Cup soccer tournament and because airlines added capacity on international routes.

Delta’s comments came three weeks after Deutsche Lufthansa AG cut its forecast for 2014-2015 earnings. The German carrier said that excess capacity from Persian Gulf airlines was causing prices to fall on trans-Atlantic routes.

Analysts largely stood by Delta. Cowen and Co. analyst Helane Becker, for example, said the June revenue figure was “a little lower than expected.” But she predicted that business travel to Brazil will recover after the World Cup — being played in several Brazilian cities — ends on July 13.

Stifel analyst Joseph DeNardi said that Delta’s lower forecast of profit-sharing expense, disclosed in a regulatory filing, suggested that the airline was taking “a more cautious view” about profits in the second half of the year. Still, he slightly raised his estimate of 2014 earnings based on better margins.

Moody’s Investors Service also upgraded Delta’s corporate credit rating one notch, to Ba3 from B1, citing expectations of higher earnings. That rating is still considered speculative.

Moody’s analyst Jonathan Root predicted that Delta will boost earnings and spend less on new planes than United and American in the coming years.

The Atlanta-based airline said that June traffic rose 3 percent as passengers flew 19.03 billion miles last month, with domestic traffic up 3.9 percent and international up 1.9 percent. Delta boosted passenger-carrying capacity by 3.1 percent, with most of the increase on international routes. The average flight was 87.5 percent full, unchanged from June 2013.

All the numbers included flights on Delta and its Delta Connection affiliate.

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Photo Credit: A passenger waits for his flight near a Delta Air Lines logo at Detriot Airport November 20, 2010. Sim Wei Yang / Reuters