Less than a week before Spirit shareholders are set to vote on the deal, Frontier Airlines sweetened its offer.
The new offer for $4.13 per share is $2 per share higher than Frontier's original cash and stock bid.
In the last few weeks, the battle for the company has intensified. The deal would allow it to compete against large carriers and grow quickly when there is a shortage of pilots.
The combination of Frontier andSpirit would create a discount carrier. The country's fifth- largest airline would be created by either transaction.
The Frontier deal will be put to a vote at the shareholder meeting.
Ted Christie told CNBC that the airline's board has doubts about regulators approving the deal. He said that the board still sees a Frontier tie-up as a superior transaction.
The airline didn't say anything.
The reverse break-up fee has been increased to $350 million if the deal isn't approved by regulators. That's in line with the reverse break-up fee offered by the airline. A pre-payable amount of $2.22 was included in Frontier's offer.
The board still had regulatory concerns about the Northeast Alliance, which allows the carriers to coordinate on flights and book passengers on each other's planes. The partnership was sued by the justice department.
The airlines' shares were lower after the market closed.