Delta Air Lines Inc. said Wednesday that lower fuel prices led to better-than-expected earnings in its June quarter, though unit revenue fell more than the company had forecast.

Shares increased about 3% in premarket trading.

U.S. airline stocks have been volatile, and investors had bid them up for most of the past year on hopes the companies would continue reaping the benefits of cheap fuel without engaging in the competition that has hurt their profits in the past.

Delta has continued to benefit from sharply falling oil prices. Fuel expense in the latest quarter fell $463 million from the year before due to a 39% drop in market fuel prices that helped offset nearly $600 million in settled hedge losses.

For the latter half of 2015, the company expects fuel price of $1.90 to $2 a gallon, down from $2.65 a year earlier. For the current quarter, the company expects 30% fuel savings.

Meanwhile, Delta said its passenger unit revenues fell 4.6% on a 3.9% decline in yields. The carrier in July had forecast a 4.5% unit-revenue decline.

Unit revenue is a closely watched airline metric that measures revenue per seat flown a mile. It has been expected to decline for virtually all U.S. carriers in the second quarter because of heightened capacity, softened domestic demand and foreign-exchange pressures.

On Wednesday, Delta said it expects unit revenue to fall 4.5% to 6.5% in the current quarter.

Delta President Ed Bastian said that "unit revenue growth is an important component of our long-term plan to expand margins." The company expects flat system capacity growth for the fourth quarter of 2015, "a level in line with current demand expectations, which should put the business on the right trajectory to stem the erosion in unit revenues by the end of the year," he said.

Delta also forecast capacity growth of about 3% in the third quarter compared with the year-earlier period.

The Justice Department recently said that it is investigating whether U.S. airlines, including Delta, colluded on expansion plans, amid concerns from consumer advocates and politicians that the industry is trying to extend its recent run of prosperity by controlling capacity to keep airfares high.

Overall, Delta reported $1.49 billion of earnings, or $1.83 a share, up from $801 million, or 94 cents a share, a year earlier. Excluding special items, per-share earnings were $1.27 a share.

Revenue rose to $10.71 billion from $10.62 billion.

Analysts had expected earnings of $1.21 a share on sales of $10.65 billion.

Write to Angela Chen at angela.chen@wsj.com

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