Delta Air Lines Inc., the nation’s third biggest carrier, cut its fares on Wednesday by up to 50 percent for travel in the continental U.S., prompting fears of a new fare war and sending its shares sharply lower.

The Atlanta-based airline, which is restructuring to try to avoid filing for bankruptcy, said that no one-way economy fare would be higher than $499 and no one-way first-class fare would be higher than $599. It is also eliminating a rule that requires a Saturday-night stay.

The company said the new fare program, dubbed “SimpliFares,” would reduce fees for changing tickets by half, to $50 from $100.

Analysts said other carriers will likely have to match Delta’s cuts, forecasting a gloomy year for the airline industry.

Delta shares fell 51 cents, or 7 percent, to $6.80 by close of trading.