The directors are urging shareholders to instead vote for a $2.9 billion merger with

Frontier.

Spirit Chairman Mac Gardner said that JetBlue’s offer hasn’t addressed the risk that the deal may not get past the finish line and that doesn’t offer enough protections for Spirit shareholders.

“The proposed combination of JetBlue and Spirit lacks any realistic likelihood of obtaining regulatory approval, while our company faces a long and bleak limbo period as we await resolution,” he said in a statement.

Shares of all three airlines fell slightly in premarket trading.

The rival low-cost carriers have been playing tug of war over Spirit, which rejected JetBlue’s offer for a $3.6 billion acquisition over concerns that the deal would be blocked by antitrust regulators.

JetBlue on Monday launched its hostile takeover attempt for Spirit, taking its case directly to shareholders in an attempt to pressure Spirit management to re-engage in negotiation.

Spirit agreed in February to be acquired by fellow low-cost airline Frontier in a cash-and-stock deal. Both airlines cater to budget-conscious travelers with low base fares and fees for everything else, from bottled water to carry-on bags.

JetBlue later came in with a higher offer, arguing that a combination of JetBlue and Spirit would create a more formidable competitor to the current airline market.

Spirit has continued to stick with the Frontier offer, over regulatory concerns that a combination with JetBlue would be blocked. JetBlue has pledged to shed assets to win regulatory approval and pay a $200 million breakup fee if it is unable to complete the proposed deal due to antitrust concerns.

Write to Dean Seal at dean.seal@wsj.com