Delta spokeswoman Keyra Lynn Johnson said 2,000 workers signed up for an early job buyout program, but the reduction did not go as far as needed to keep operating costs as far down as the airline required, The Atlanta Journal-Constitution reported.
"We're not simply reducing headcount. We're reducing costs as a whole as part of the pressures of high fuel costs," Johnson said.
"Reducing headcount involuntarily at Delta is truly something that we look to as a last resort," she added.
Delta currently employs about 80,000 people, the newspaper said.