Australia's richest woman Gina Rinehart is in the box seat to buy the country's largest private land holding, cattle and pastoral tracts the size of South Korea, after a rival bidder dropped out.

The BBHO consortium - made up of a group of outback cattle families - said on Friday it was withdrawing its A$386 million ($293 million) offer for S. Kidman & Co. despite receiving a "strong groundswell of public support."

The decision follows a pledge by Rinehart a day earlier to buy the land holdings outright if her A$386.5 million joint bid with Chinese partner Shanghai CRED, which requires approval by Australia's Foreign Investment Review Board (FIRB), was rejected on national interest grounds.

A source close to the bidding process told Reuters that Rinehart's undertaking to buy S. Kidman alone if necessary killed off the BBHO bid, which was relying on its all-Australian status.

"That was decisive," the source said. "If they had continued it would have resulted in a financial shoot-out they couldn't win."

Ownership of S. Kidman has been a lightning rod for concerns about the sale of Australian agriculture and other key assets to foreign investors.

Federal Treasurer Scott Morrison twice blocked it’s the sale to China-led interests, opening the way for rival offers including those lodged by Rinehart and BBHO.

"We are disciplined investors in Australian rural assets and made what we believed to be a full and fair offer," the BBHO consortium, comprising cattlemen Tom Brinkworth, Sterling Buntine, Malcolm Harris and Viv Oldfield, said in a statement.

Rinehart is Australia's richest woman with a net worth of $11.7 billion, according to Forbes, based on an iron ore empire in Australia's mineral-rich Pilbara, where she grew up.

Bidders could still lodge a competing offer before the Dec. 9 deadline. ($1 = 1.3180 Australian dollars)