DALLAS (AP) -- Elliott Investment Management, a hedge fund urging Southwest Airlines to dump its CEO and chairman, said Tuesday it has acquired enough of the company's stock to call a special meeting of shareholders.

The move gives Elliott, the Paul Singer-led investment fund, more leverage in its proxy fight heading into a meeting with Southwest officials next Monday.

Elliott said in a regulatory filing that it owns more than 61 million shares, at least 10% of Southwest, the nation's fourth-largest airline by revenue. Under Southwest's bylaws, that gives Elliott the power to call a meeting at which shareholders could vote on board candidates.

Elliott has proposed a slate of 10 candidates, including former CEOs of other airlines, for Southwest's 15-member board.

"We remain prepared to meet with Elliott next week and look forward to sharing details on our continued transformation at our Investor Day on Sept. 26," a Southwest spokesperson said in a statement.

Elliott announced in June its plan to shake up Southwest, which has seen its shares lose more than half their value in the past three years. The hedge fund says Southwest's leadership has failed to evolve with the airline business, and it wants to replace CEO Robert Jordan and Chairman Gary Kelly, the previous CEO.

Southwest says changes are coming that will improve its financial performance.

The Dallas-based airline announced in July that it plans to drop open-boarding and begin assigning passengers to seats. Southwest also plans to charge extra for premium seats with more legroom. Both moves will make Southwest more like its closest rivals.

Southwest promised to give more details about the changes at the investor day later this month.