An all-Australian consortium comprising some of the country's richest grazier families made a counter-offer Sunday for one of the world's largest cattle estates, sparking a bidding war with a Chinese-linked proposal.

The sale of Australia's biggest private landowner, cattle firm S. Kidman and Co, has attracted keen interest from Chinese companies. But the government has rejected two Chinese-led bids, citing the national interest.

The new Aus$386 million (US$294 million) offer announced late Sunday came just two weeks after Australian mining magnate Gina Rinehart and Chinese property developer Shanghai CRED announced a joint Aus$365 million bid.

"We have developed a compelling and superior proposal to that recently supported by the Kidman board which will see Kidman 100 percent Australian-owned," one of the pastoralists Sterling Buntine said in a statement.

"BBHO's (the consortium) financing is committed and our proposal does not require Foreign Investment Review Board approval, which means greater certainty for the Kidman shareholders.

"The four families comprising the consortium are deeply committed to honouring and preserving the Kidman heritage and brand which will continue under the stewardship of highly regarded and successful Australian graziers."

The other consortium members are Tom Brinkworth, Malcolm Harris and Viv Oldfield, all of whom have sizable properties across the vast island continent.

Under the Australian proposal, Anna Creek station in South Australia -- which is next to a rocket testing range -- is included in the deal.

Anna Creek was removed from sale after the first Chinese-led bid was rejected last November. Canberra cited the sensitive location of the station, which has about half of its pastoral lease in a weapons testing range.

There had been optimism that Rinehart's Hancock Prospecting joint offer with Shanghai CRED, which would see her firm acquire 67 percent of Kidman with the Chinese company holding 33 percent, would get the green light from Canberra.

Shanghai CRED was part of a Chinese consortium involved in the previous offers. But the Chinese stake in the current bid would be significantly smaller than previously.

Kidman, founded in 1899, holds around 1.3 percent of Australia's total land area, and 2.5 percent of the nation's agricultural land. It is currently 33.9 percent foreign-owned.

It is a key source of beef for export to Japan, the United States and Southeast Asia.

There has been growing concern in Australia about the purchase of local infrastructure and land by foreign interests.

An all-Australian consortium bought half of the nation's largest electricity network on Thursday after Canberra rejected a Chinese bid, citing national security.