Southwest Airlines Co's mechanics, who have been in labor contract talks for more than six years, deserve a new deal that makes them among the best paid in the airline industry, but the low-cost U.S. carrier needs "more supplier flexibility" in return, the company's chief executive said.

The labor dispute, one of the biggest to hit a top-four U.S. airline in more than a decade, has escalated with Southwest's daily out-of-service aircraft doubling, forcing the carrier to cancel hundreds of flights since Feb. 15.

Southwest CEO Gary Kelly in an email to the company's employees acknowledged the company was "in a period of tension and turmoil" regarding the out-of-service aircraft. Reuters obtained a copy of the email late Friday.

Kelly said the mechanics deserve a new contract and pointed out that the deal the mechanics voted down last year would have made those workers the highest paid in the industry. He said current talks offer the opportunity to offer even higher pay with no impact on job security "in exchange for more supplier flexibility."

Southwest already outsources the majority of heavy maintenance work, such as scheduled engine repairs, to external suppliers, but wants the option to send more scheduled maintenance abroad in order to fund compensation increases. The change would not affect the kind of work currently handled by its mechanics, a Southwest spokesman said.

Officials with the Aircraft Mechanics Fraternal Association (AMFA), which represents about 2,400 Southwest mechanics and has been in contract talks with management since 2012, could not immediately be reached to comment on Saturday.

The union has disputed the notion that the maintenance issues are driven by the labor dispute, pointing out the company has the lowest mechanic-to-aircraft ratio of any major carrier.

In a Friday email to its members, the union rejected the company's assertion that the maintenance issues were a job action and said mechanics should not allow themselves to be pressured to ignore safety or mechanical issues with a plane.

"If you feel you are being pressured to disregard aircraft damage or shortcut the manuals, then let your airline representative know of such threats," union national director Bret Oestreich said in the email. "But do not get baited into acts of defiance that will be characterized as insubordination."

Flights by Southwest accounted for more than a third of 777 U.S. cancellations between Friday and Saturday, according to FlightAware.com.