The next-largest carrier is Southwest Airlines, which is less then one-eighth the size with about 9.4 percent of the market, according to the most recent figures for the year-to-date.
Meanwhile, two ultra low-cost carriers, Frontier and Spirit, are seeking to grow a toe-hold in Atlanta.
During Delta's annual investor day on Thursday, CEO Richard Anderson said: "We have the most profitable hub in the world in Atlanta, with huge scale." Atlanta is also the world's largest airline hub.
Delta said its growth in its flight schedule next year will range from 0 to 2 percent. The airline plans to grow slightly more domestically at 1 to 3 percent, which will be "very targeted in the areas of strength," including New York, Seattle, Los Angeles and Atlanta, said Delta president Ed Bastian.
"We're going to be leveraging scale," Bastian said. "That's where we're going to be growing."
Anderson said Delta's Atlanta operation requires a roughly $100 million investment annually, noting that the airport plans to build a sixth runway and add more concourses as needed.
Delta is in negotiations with the city of Atlanta for a 20-year lease at Hartsfield-Jackson International Airport, which wraps in discussions about airport expansion in the airport's $6 billion master plan.
Atlanta Mayor Kasim Reed said efforts are underway to reach a lease deal.
“Over a 20 year period of time on a $6 billion dollar deal, you have to make sure the revenue flows right, rise and fall at the same time consistent with the projects going on at the time," Reed said. "That’s what makes it challenging, a 20 year horizon.”
Reed said he sees a 20-year deal as important because "we’re in such a competitive environment nationally and internationally that I’d like to see the relationship between Delta and the City of Atlanta be one that’s not be in flux."
Atlanta Journal-Constitution reporter Katie Leslie contributed to this report.