The Atlanta-based carrier also reported a hit to transatlantic bookings as travelers are avoiding Paris due to the Olympic Games this summer.
Delta shares were trading at $42.65, while rivals United Airlines (UAL.O) and American Airlines (AAL.O) were down nearly 6% each.
Domestic peer Southwest Airlines was also down 3%, while European rivals Lufthansa (LHAG.DE) and British Airways owner IAG (ICAG.L) fell between 1% and 2%.
Delta forecast an adjusted profit between $1.70 and $2.00 per share in the third quarter through September compared with analysts' expectations of $2.05, according to LSEG data.
Airlines are enjoying a summer travel boom, with more than 3 million people passing through U.S. airport security checkpoints in a single day on July 7.
The boom has failed to lift earnings at most of the U.S. carriers as excess industry capacity has undermined pricing power. Major airlines have scheduled about 6% more seats in the domestic market this month than a year earlier, data from consultancy Cirium shows.
Average round-trip ticket price for a U.S. domestic flight was $543 in May, down 1% month-on-month and 3% lower from a year earlier, according to data from Airlines Reporting Corporation (ARC).
American Airlines (AAL.O) and Southwest (LUV.N) have cut their revenue forecasts in the second quarter, citing discounting pressure.
Delta's revenue from main cabins, which generate about 49% of its passenger revenue, was flat in the June quarter. In contrast, revenue from premium cabins was up 10% year-on-year.
"This (Delta's earnings) print will likely raise concerns about industry health and lead to more pressure on low-cost carriers and ultra-low-cost carriers to cut capacity," TD Cowen analysts said.
Delta expects its annual seat capacity growth to be 5%-6% in the third quarter, compared with an 8% growth in the second quarter. The moderation in capacity growth, however, is estimated to drive up its non-fuel operating costs by 1%-2% year-on-year.
The airline said its revenue suffered in the June quarter due to the upcoming Olympic Games in Paris. Analysts and industry officials expect the impact to persist in the current quarter as high costs and safety worries are discouraging many international travelers from visiting the French capital.
Last week, Air France-KLM (AIRF.PA) warned of a 160 million to 180 million euros ($173 million to $194.81 million) hit to its unit revenue between June and August, saying international markets were avoiding Paris.
Delta expects to post an operating margin of 11%-13% in the third quarter, with a 2%-4% year-on-year increase in revenue.
It reported an adjusted profit of $2.36 a share for the second quarter, in line with analysts' estimates. The company reaffirmed its forecast for a profit of $6 to $7 per share in 2024 with a free cash flow of $3 billion-$4 billion.
For the second quarter, Delta posted an adjusted operating revenue of $15.41 billion, compared with analysts' expectations of $15.45 billion.
($1 = 0.9240 euros)
