Stewart said Southwest has scheduled several meetings this summer with minority business groups.
In Washington, Rep. Eddie Bernice Johnson, D-Dallas, told the Star-Telegram that she wants to arrange a meeting between the mayors of Fort Worth and Dallas to settle differences over the Wright Amendment.
She said she has been in contact with the municipal leaders, but no date has been set.
Johnson said she has not taken a position in the Wright Amendment debate, saying "there are good points on both sides."
Dallas Mayor Laura Miller said she supports a meeting with elected officials to seek a solution to the Wright Amendment issue. "A local solution is best," she said.
Johnson had earlier suggested a meeting that would include the leadership of American and Southwest. But she said on Wednesday that she has scrapped that idea because it could violate federal antitrust rules.
Gerard Arpey, chief executive of American Airlines, agreed. "I don't think the Justice Department or the Transportation Department would look favorably upon us being in the same room with Southwest Airlines," he said.
Arpey was in Washington along with more than 300 American Airlines executives and workers to tout the company's position on pension rules. But Arpey said he also used his visits with House and Senate members to "weigh in" with the company's opposition to repealing the Wright Amendment.
Star-Telegram Washington Reporter Dave Montgomery and Staff Writer Nathaniel Jones contributed to this report.
A citizens committee representing neighborhoods around Dallas Love Field said it would withdraw support for the city's airport master plan if the Wright Amendment is repealed.
Dallas Love Field could see traffic double or even triple if the Wright Amendment were repealed.
A consultant hired by Dallas-Fort Worth International Airport says an expansion of nearby Love Field would lead to reduced flights and millions fewer passengers each year at DFW.