South Korean budget airline Jeju Air Co Ltd signed a preliminary deal to buy a 51% stake in unlisted low-cost carrier Eastar Jet Co for about 69.5 billion won (US$58.93 million), Jeju Air and its parent AK Holdings said on Wednesday.

The deal shows consolidation is underway in South Korea's crowded budget carrier space as travel demand is falling to the key Japan market due to a diplomatic row between the two neighboring countries, hitting profitability of airlines.

The news of a majority stake sale in Eastar Jet came after Eastar asked cabin crew members earlier this year to take unpaid leaves as part of emergency cost-cutting plans to help it keep flying. The carrier's losses had risen as demand for travel to Japan fell and as its two Boeing 737 MAX jets were grounded.

South Korea currently has six budget carriers operating, with three more expected to launch next year.

Jeju Air, the country's largest budget carrier, said in a statement it expected to sign a final deal by the end of this year. Jeju Air's shares rose as much as 13% on Wednesday.

Eastar Jet currently operates 34 routes with 23 aircraft, including the two grounded Boeing 737 MAX 8.