DALLAS >> Already struggling with high fuel prices, the big U.S. airlines now face a drop in demand for flights to Japan, a lucrative route and gateway for travel to Asia.

The airlines’ response: They’re raising fares and eliminating unprofitable flights.

Delta Air Lines Inc. said yesterday it will reduce flying to Japan by up to 20 percent through May because of falling demand as the country recovers from the March 11 earthquake and tsunami. Delta said the cuts will cost it $250 million to $400 million in lost profit.

Delta will also reduce flying across the Atlantic and within the United States in the second half of this year. It won’t grow as much as planned in Latin America and the Pacific.

(Spokeswoman Gina Laughlin of Delta said it was too early to tell whether Hawaii would be affected because fall and winter schedules, which are when specific changes will be announced, haven’t been published yet.)

American Airlines said yesterday that it suffered “a modest decline” in revenue from the disruption of travel to Japan and bad weather at home. Still, American plans to push ahead with its joint venture with Japan Airlines next month.

United and Continental announced Monday that they too will slow their plans for adding international flights and make deeper cuts in the U.S.

The airlines had hoped to build on 2010, their first profitable year since 2007, by flying more passengers, particularly big-spending corporate travelers buzzing to business hubs such as Tokyo. Instead, they’re being forced to make up for a sharp increase in jet fuel prices — up nearly half since September and about 20 percent since the start of 2011.

Delta said yesterday that at current projected prices, it will spend $3 billion more on fuel this year than it did in 2010.

With fewer flights, the airlines will save money by not burning as much fuel. They are also offsetting high fuel costs by raising prices on passengers.

United and Continental raised fares Monday on most U.S. flights by $10 per round trip. Delta responded with fare hikes of $6 to $14 per round trip. Other airlines stood pat for the moment.

If the higher prices stick, they would be the latest in a string of increases — nearly one a week — so far this year.

Higher prices have helped Southwest — apparently without driving away passengers. In February, Southwest customers flew 13 percent more than they did a year earlier.

“We’ve had six fare increases so far this year. That’s a lot in 90 days,” Southwest CEO Gary C. Kelly said at a JPMorgan conference in New York. “On the other hand, our traffic has held up more than well — it’s been very, very strong.”

Fare increases alone won’t solve the airlines’ cost problems, said Delta President Edward Bastian. He said his airline must save money by reducing flights and grounding 120 gas-guzzling planes, half of them 50-seat jets used on short hops.

Delta, the world’s second-largest airline company behind United Continental Holdings Inc., now plans to cut passenger-carrying capacity by 4 percentage points in the second half of this year. It will slash departures at its Memphis hub by 25 percent.

Most of Delta’s reduction in flying will fall on Japan. It is suspending flights to Tokyo’s Haneda Airport but promises to restore the serv­ice as demand recovers. Delta also flies to Nagoya and Osaka.