NEW YORK >> Elliott Investment Management and Southwest Airlines will meet early next month for the first time to discuss potential changes at the airline, both companies said on Monday, but the hedge fund told investors it may still press ahead with a proxy fight.

The activist hedge fund, which now holds voting power over roughly 9.7% of Southwest Airlines, said it is eager to meet with company representatives on Sept. 9 to discuss ways to tackle the carrier’s “immense” challenges.

The company said it is prepared to meet with Elliott on Sept. 9 and has gathered feedback in the last several months and met with many shareholders directly.

“We welcome the opportunity to discuss ideas that would drive sustained Shareholder value as we work to reach a collaborative resolution,” Southwest said in a statement. The company will also hold an investor day on Sept 26.

Elliott told its investors in a letter that the company needs new outside leadership for a “better future,” and that it could call a special shareholder meeting to vote for new board directors. If Southwest leaders cannot identify “what is best for Southwest” and its stakeholders, the hedge fund will push ahead with its board challenge, the letter said.

The hedge fund also dialed up the pressure on the airline by proposing a new board-level committee that would conduct a thorough business review and “drive transformational change.”

An investor would need to own 10% of Southwest’s stock to call a special shareholder meeting, and Elliott is very close to that point now, having increased its stake from 8% previously.

TURNAROUND PLAN

Elliott has been pushing to refresh the board and oust top executives to help improve the carrier’s performance. In June, CEO Bob Jordan said Southwest has a “great plan,” which management will execute,” and that he had no plans to resign.

The airline has been trying to implement a turnaround plan, including adding seats with more leg room, moving to assigned seats and naming a new board member in July. Its stock price, which has been under pressure, pared losses recently.

Southwest’s stock closed largely unchanged at $28.20.

Earlier this month, Elliott laid out plans to nominate 10 director candidates to Southwest’s 15-person board, including former Virgin America CEO David Cush and Robert Milton, the former CEO of Air Canada.

In the letter, Elliott said why it wants so many board seats. The hedge fund does not want to be “in charge” but said the board is “purpose-built to serve the interests” of CEO Robert Jordan and his predecessor and current executive chairman Gary Kelly. Elliott has pushed for Jordan and Kelly to be replaced since its stake in the airline became public in June.

As a public company, Elliott wrote, Southwest must be accountable to shareholders and is not “an absolute monarchy.”

Some investors share Elliott’s frustration, the letter said, noting that Artisan Partners publicly called for leadership change and urged the board to work with Elliott. Other shareholders expressed concerns privately to the hedge fund, it wrote.

The hedge fund also pointed to concerns among Southwest pilots who have called for bold leadership to fix corporate problems.

The airline must find a comprehensive solution, “not just some hand-picked new directors beholden to current management and a few long-overdue initiatives,” the letter said.

While CEO Jordan recently wrote that the fight with Elliott is “a battle for the heart of our company,” the hedge fund said it is a fight for Jordan and Kelly to “continue to control Southwest, on their terms, for as long as they wish.”