NEW YORK, Aug 26 (Reuters) - Elliott Investment

Management is telling Southwest Airlines ( LUV ) investors the

company needs new outside leadership and that it wants to engage

to shape a "better future" but is also ready to press ahead with

a planned proxy fight.

In a letter to shareholders, seen by Reuters, Elliott is

dialing up the pressure on the airline by proposing a new

board-level committee that would conduct a thorough business

review and "drive transformational change."

The hedge fund said it is eager to meet with company

representatives on Sept. 9 to discuss ways to tackle the

company's "immense" challenges. But Elliott also warned that if

leaders cannot identify "what is best for Southwest ( LUV )" and its

stakeholders, it will push ahead with a board challenge.

Elliott has been pushing to refresh the board and oust top

executives to help improve the carrier's performance.

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.

A representative for Southwest ( LUV ) was not immediately available

for comment.

Earlier this month, Elliott laid out plans to nominate 10

director candidates to Southwest's ( LUV ) 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. It does not want to be "in charge" but feels the board is

"purpose-built to serve the interests" of CEO Robert Jordan and

his predecessor and current executive chairman Gary Kelly. The

hedge fund 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 ( LUV ) must be

accountable to shareholders and is not "an absolute monarchy."

Elliott owns roughly 8% of Southwest's ( LUV ) outstanding shares,

according to a recent regulatory filing. Including derivatives,

the hedge fund has an economic interest of 11% in the carrier.

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.

Elliott also pointed to frustration among Southwest ( LUV ) 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 ( LUV ), on their terms, for as long as they wish."

Elliott has said it is preparing to call a special

shareholder meeting where investors would have a chance to vote

on directors.

(Reporting by Svea Herbst-Bayliss; Editing by Muralikumar

Anantharaman)