BERLIN—Volkswagen AG shares fell sharply in early trade on Thursday after the car maker reported a 56% drop in after-tax profit in the three months to the end of June, hit by rising costs as the company struggles to move past its crippling emissions-cheating scandal.

The Wolfsburg, Germany-based car maker, which outpaced rivals Toyota Motor Corp. and General Motors Co. in sales in the first six months of the year, said after-tax profit fell to €1.2 billion ($1.33 billion) in the second quarter from €2.7 billion a year ago.

The company's shares fell more than 3% to about €124 in early trading on the Frankfurt Stock Exchange.

Volkswagen said revenue in the three-month period was €56.9 billion, up 1.7% from €56 billion the year before. Operating profit, as reported in a pre-release on July 20, surged nearly 20% to €4.4 billion. That was halved, however, by charges of €2.5 billion, largely related to the diesel scandal. Volkswagen's Thursday release provided details not included in the July 20 advance release of headline profit figures that beat analysts' forecasts.

"This shows that the Volkswagen Group has high earnings power. But it will require continued hard work to absorb the significant impact from the diesel issue," said Chief Finance Officer Frank Witter in a statement.

U.S. environmental authorities disclosed in September that Volkswagen had been cheating on emissions tests for years by rigging diesel engines to produce lower emissions when being tested than during normal driving, forcing a sweeping shake-up of management and plunging the company into turmoil.

On Wednesday, a U.S. federal court gave preliminary approval to Volkswagen's $15 billion settlement with U.S. customers, environmental authorities and state attorneys general, the largest class-action settlement ever reached with an auto maker. Final approval is expected in October.

Volkswagen had set aside €16.2, nearly $18 billion, in its 2015 accounts to pay for compensating cheated customers, legal fees and other costs related to the scandal.

The company said in April that it didn't expect further diesel-related costs. The second-quarter charges, though significantly lower than those taken last year, suggest that the company has underestimated the full cost of its diesel scandal.

Czech car maker Skoda, Spain's SEAT, Porsche and the company's truck division drove Volkswagen's automotive operating profit higher, compensating for declining earnings at Audi, the Volkswagen passenger car brand, and Bentley.

Lower earnings from its joint ventures in China, the car maker's biggest market by sales, also hit Volkswagen earnings. Profit from China is booked as a financial gain, so it doesn't appear in operating earnings. Volkswagen said China's contribution to earnings fell to €2.4 billion from €2.7 billion in the first half of the year.

Despite the emissions-cheating crisis, Volkswagen sold more vehicles in the first half of the year and outpaced rivals Toyota and GM to remain the biggest auto maker in the world by sales.

Volkswagen sales rose 1.5% in the six months to the end of June to 5.1 million vehicles, including its namesake Volkswagen brand, Audi luxury cars, Porsche sports cars, Skoda, SEAT, Bentley and Lamborghini.

Toyota, which held the industry crown last year, sold 4.99 million vehicles in the first half of 2016, down 0.6%, and GM sold 4.76 million vehicles world-wide.

Write to William Boston at william.boston@wsj.com

(END) Dow Jones Newswires

July 28, 2016 05:25 ET (09:25 GMT)