Many industry observers have speculated that Frontier and Spirit would make good merger partners because of their similar business models, complementary networks and friendly management teams. Mr. Franke stoked speculation in January when he said at an aviation conference that there is room for consolidation among U.S. low-cost carriers.

He reiterated that point earlier this month. “I do believe there will be additional consolidation” among a group of airlines that includes Frontier, Spirit, JetBlue Airways Corp., Alaska Air Group Inc. and Virgin America Inc., he said.

Spirit said in a statement: “We are focused on native growth and we have no plans for merging with any other airline.”

Mr. Franke agreed that a Spirit-Frontier merger isn’t imminent. “Right now they both have a fairly aggressive independent position,” he said. “While we obviously know Spirit management well…there hasn’t really been any formal discussion about the combination of the two airlines.”

Mr. Biffle, Frontier’s president, was blunter: “We have spent zero effort” on consolidation.